Final Exam Revision T3-2025

Multiple Choice

$$\frac{\text{d}}{\text{d}x}\left(x^2\right)=?$$  

• $$2x$$  

• $$x^2$$  

• 1

• 0

THEOREM

2.4

THE PRODUCT AND QUOTIENT RULES

4.2

Slide 9

(Quotient Rule)

Fill in the Blank

$$\frac{\text{d}}{\text{d}x}\left(x^3\right)=?$$  

Multiple Choice

Find the derivative of the given equation: $$f\left(x\right)=-4x$$

• $$f'\left(x\right)=4$$  

• $$f'\left(x\right)=x$$  

• $$f'\left(x\right)=-4$$  

• $$f'\left(x\right)=0$$  

Multiple Choice

Find the derivative of the given equation: $$f\left(x\right)=7$$

• $$f'\left(x\right)=\frac{7}{x}$$  

• $$f'\left(x\right)=0$$  

• $$f'\left(x\right)=7x$$  

• $$f'\left(x\right)=-\frac{7}{x}$$  

Multiple Choice

Find the derivative of the given equation: $$f\left(x\right)=12-8x$$  

• $$f'\left(x\right)=12-8x^2$$

• $$f'\left(x\right)=-8x^2$$

• $$f'\left(x\right)=-8$$
  

• $$f'\left(x\right)=4$$
  

Multiple Choice

Find the derivative of the given function: $$f\left(x\right)=x^4$$

• $$f\left(x\right)=x^3$$  

• $$f'\left(x\right)=4x$$  

• $$f'\left(x\right)=4x^3$$  

• $$f\left(x\right)=4x^4$$  

Multiple Choice

Find the derivative of the function: $$f\left(x\right)=-\frac{10}{3}$$  

• $$f'\left(x\right)=-\frac{10}{3x}$$  

• $$f'\left(x\right)=-\frac{10x}{3}$$  

• $$f'\left(x\right)=\frac{10x}{3}$$  

• $$f'\left(x\right)=0$$  

Multiple Choice

Find the derivative of the given function: $$f\left(x\right)=1-x^2$$

• $$f'\left(x\right)=1-2x$$  

• $$f'\left(x\right)=-2x$$  

• $$f'\left(x\right)=-2$$  

• $$f'\left(x\right)=0$$  

Multiple Choice

Find the derivative of the given function: $$f\left(x\right)=x^3+x^2+3$$

• $$f'\left(x\right)=3x^2+2x$$  

• $$f'\left(x\right)=5x$$  

• $$f'\left(x\right)=5x+3$$  

• $$f'\left(x\right)=x^3+x^2$$  

Multiple Choice

Find the derivative of the given function:
$$f\left(x\right)=\frac{1}{x^2}$$

• $$f'\left(x\right)=\frac{1}{2x}$$  

• $$f'\left(x\right)=-\frac{2}{x^3}$$  

• $$f'\left(x\right)=-\frac{2}{x}$$  

• $$f'\left(x\right)=-\frac{1}{2x^3}$$  

Multiple Choice

Find the derivative of $$y=\frac{12}{x^2}$$  

• ^{$$y'=\frac{24}{x}$$}  

• ^{$$y'=-\frac{24}{x^3}$$}  

• ^{$$y'=-\frac{24}{x}$$}  

• ^{$$y'=\frac{6}{x^3}$$}  

Multiple Choice

Find the derivative of $$y=4x^3+3x+10$$

• $$\frac{dy}{dx}=4x^2+3$$  

• $$\frac{dy}{dx}=4x^2+3x$$  

• $$\frac{dy}{dx}=12x^2+3x$$  

• $$\frac{dy}{dx}=12x^2+3$$  

Multiple Choice

Find the derivative of  $$y=\frac{2x^2+x-3}{x}$$  

• $$y'=2x+1-\frac{3}{x}$$  
  

• $$y'=4x+1-\frac{1}{x^2}$$  
  

• $$y'=2+\frac{3}{x^2}$$  
  

• $$y'=2-\frac{3}{x^2}$$  
  

Multiple Choice

Find the derivative of the function: $$f\left(x\right)=\sqrt{x^5}$$  

• $$f'\left(x\right)=\frac{5}{2\sqrt{x^3}}$$  

• $$f'\left(x\right)=\frac{5\sqrt{x^3}}{2}$$  

• $$f'\left(x\right)=-\frac{5}{2\sqrt{x^3}}$$  

• $$f'\left(x\right)=-\frac{5\sqrt{x^3}}{2}$$  

Multiple Choice

Find the derivative of the function: $$f\left(x\right)=\frac{1}{\sqrt{x^3}}$$

• $$f'\left(x\right)=-\frac{3}{2\sqrt{x^5}}$$  

• $$f'\left(x\right)=-\frac{2}{3\sqrt{x^5}}$$  

• $$f'\left(x\right)=-\frac{3}{\sqrt{x}}$$  

• $$f'\left(x\right)=-\frac{3}{2\sqrt{x}}$$  

THEOREM

2.4

THE PRODUCT AND QUOTIENT RULES

4.1

Slide 5

(Product Rule)

Multiple Choice

Which one is the product rule?

• $$f\left(x\right)g\left(x\right)$$  

• $$f'(x)g(x)-f(x)g'(x)$$  

• $$f'(x)g(x)+f(x)g'(x)$$  

• $$f'(x)g'(x)+f(x)g(x)$$  

Multiple Choice

Use the product rule to find the derivative. $$f\left(x\right)\ =\ -x^3\left(3x^4-2\right)$$  

• $$-3x^2+12x^3$$  

• $$-21x^3+6x$$  

• $$-21x^6+6x^2$$  

• $$-84x^6-6x^2$$  

Multiple Choice

Find the derivative of

$$x^2\left(-3x^2-2\right)$$  

• $$-6x^3-4x$$  

• $$-12x^3-4x$$  

• $$12x^3+4x$$  

• $$-36x^2-4$$  

Multiple Choice

Find the derivative of $$f\left(x\right)=\left(-x^3-2\right)\left(-4x^2-1\right)$$ . 

• $$12x^4+3x^2$$  

• $$20x^4+3x^2+16x$$  

• $$3x^5+32x^3+6x^2+8x$$  

• $$24x^3$$  

Poll

How much Do you rate Your understanding of Product Rule and application of Derivatives.

• 100%

• Good Understanding

• Average Understanding

• Lesson Not Understood

THEOREM

2.4

THE PRODUCT AND QUOTIENT RULES

4.2

Slide 9

(Quotient Rule)

EXAMPLE

2.4

THE PRODUCT AND QUOTIENT RULES

4.3

Using the Quotient Rule

Slide 12

EXAMPLE

Solution

2.4

THE PRODUCT AND QUOTIENT RULES

4.3

Using the Quotient Rule

Slide 11

Multiple Choice

$$If\ y=\frac{3}{4+x^2},\ then\ \frac{dy}{dx}=$$  

• $$\frac{3}{2x}$$  

• $$\frac{3x}{\left(1+x^2\right)^2}$$  

• $$\frac{6x}{\left(4+x^2\right)^2}$$  

• $$-\frac{6x}{\left(4+x^2\right)^2}$$  

• $$-\frac{3}{\left(4+x^2\right)^2}$$  

Multiple Choice

Given that      $$y=\frac{x+2}{x-3}$$  

Find y'

• $$y'=-\frac{1}{\left(x-3\right)^2}$$  

• $$y'=-\frac{5}{\left(x-3\right)^2}$$  

• $$y'=\frac{2x-5}{\left(x-3\right)^2}$$  

• $$y'=\frac{2x-1}{\left(x-3\right)^2}$$

Multiple Choice

$$y\left(x\right)=\frac{4x^2+3}{2x^2-5}$$  

Find the derivative above.

• $$y\ '=\frac{-52x}{\left(2x^2-5\right)^2}$$  

• $$y\ '=\frac{-28x}{\left(2x^2-5\right)^2}$$

• $$y\ '=\frac{32x^3-52x+15}{\left(2x^2-5\right)^2}$$  

• $$y\ '=\frac{-10x}{\left(2x^2-5\right)^2}$$  

Multiple Choice

If $$y=\frac{4x^3}{2x^2-5}$$ , find $$\frac{dy}{dx}$$ . 

• $$8x^4-60x^2$$  

• $$16x^4$$  

• $$2-\frac{12}{5}x^2$$  

• $$\frac{8x^4-60x^2}{\left(2x^2-5\right)^2}$$  

The chain rule

by Sahel Otoom

Multiple Choice

Find the derivative of  f(x) = (x⁶ + 4)⁵

• f '(x) = 5x⁵(x⁴ + 4)⁴
• f '(x) = 6x⁵(x⁶ + 4)⁴
• f '(x) = 30x⁵(x⁶ + 4)⁴
• f '(x) = 30x⁶(x⁶ + 4)⁴

Multiple Choice

Find the derivative of f(x)=(x³-2x)²

• 6x⁵ - 12x³+8x
• 6x⁵ - 16x³+8x
• x⁶-4x⁴+4x²
• 6x⁵ - 16x^3-8x

Multiple Choice

$$y=\left(1+\sin x\right)^3$$  Differentiate

• $$3\cos x\left(1+\sin x\right)^2$$  

• $$3\left(1+\sin x\right)^2$$  

Multiple Choice

Find the derivative

Multiple Choice

Differentiate:
f(x) = x⁷ (5 + 8x)³

• f '(x) = x² (5 + 8x)⁶ (35 + 80x)
• f '(x) = x⁶ (5 + 8x)² (35 + 80x)
• f '(x) = 8x⁷ (5 + 8x)² (35 + 80x)
• f '(x) = x⁶ (5 + 8x)³ (35 + 80x)

Multiple Choice

Warm Up $$\frac{dy}{dx}\ if\ y=\left(2x^2+4\right)^3$$  

• $$\left(12x+4\right)\left(2x^2+4\right)^2$$  

• $$3\left(2x^2+4\right)^2$$  

• $$12x\left(2x^2+4\right)^2$$  

• $$12\left(2x^2+4\right)^2$$  

Multiple Choice

$$f\left(x\right)=\sqrt{x}$$   $$\frac{dy}{dx}=$$  

• $$\sqrt{x}$$  

• $$2\sqrt{x}$$  

• $$\frac{2}{\sqrt{x}}$$  

• $$\frac{1}{2\sqrt{x}}$$  

​Derivatives of Trigonometric Functions

Multiple Choice

The Dubai Metro train runs according to the function

$$f\left(x\right)=\sqrt[]{x^3+9x}$$

Find the derivative of the function?

• $$\frac{3x^2+9}{2\ \sqrt[]{x^3+9x}}$$

• $$\frac{x^2+9}{2\ \sqrt[]{x^3+9x}}$$

• $$\frac{3x^2+9x}{2\ \sqrt[]{x^3+9x}}$$

• $$\frac{3x^3+9x}{2\ \sqrt[]{x^3+9x}}$$

• $$\frac{3x^2+9}{2\ \sqrt[]{2x^3+9}}$$

Multiple Choice

$$\frac{d}{dx}\left(\sec x\right)$$

• $$\sec x\ \tan x$$

• $$\sec x$$

• $$\tan x$$

• $$-\sec x\ \tan x$$

Multiple Choice

$$\frac{d}{dx}\left(x-3\sin x\right)=$$  

• $$1-3\cos x$$  

• $$1+3\cos x$$  

• $$1-3\sin x$$  

• $$1+3\sin x$$  

Multiple Choice

$$\frac{d}{dx}\left(x\sin x\right)=$$  

• $$\cos x$$  

• $$x\sin x+\cos x$$  

• $$x\cos x+\sin x$$  

• $$x\sin x-\cos x$$  

Multiple Choice

$$\frac{d}{dx}\left(\sin x+\cos x\right)=$$  

• $$\sin x+\cos x$$  

• $$\sin x-\cos x$$  

• $$-\sin x+\cos x$$  

• $$-\sin x-\cos x$$  

Multiple Choice

$$\frac{d}{dt}\left(4\sec t+\tan t\right)=$$  

• $$4\tan t+\sec t$$  

• $$4\sec t+\tan t$$  

• $$\tan t\left(4\sec t+\tan t\right)$$  

• $$\sec t\left(4\tan t+\sec t\right)$$  

Multiple Choice

$$\frac{d}{d\theta}\left(\theta\csc\theta-\cot\theta\right)=$$  

• $$\csc\theta\left(-\theta\cot\theta+1+\csc\theta\right)$$  

• $$\csc\theta\left(-\theta\csc\theta+1+\cot\theta\right)$$  

• $$\cot\theta\left(-\theta\cot\theta+1+\csc\theta\right)$$  

• $$\cot\theta\left(-\theta\csc\theta+1+\cot\theta\right)$$  

Multiple Choice

$$\frac{d}{dx}\left(\frac{\sin x}{x^2}\right)=$$  

• $$\frac{\cos x}{2x}$$  

• $$\frac{x\cos x-2\sin x}{x^3}$$  

• $$\frac{2\cos x-x\sin x}{x^3}$$  

• $$\frac{x^2\cos x+2\sin x}{x^4}$$  

Multiple Choice

Find $$\frac{\text{d}}{\text{d}x}\left(\ 4\sin\ 6x\right)\ =$$  

• 24 cos x

• 24 sin 6x

• 24 cos 6x

• -24 cos 6x

Multiple Choice

If $$y\ =\ 3x\ -\ 5\ \cos\left(2x^2-3\right)$$  . Find $$\frac{\text{d}y}{\text{d}x}$$  .

• $$3+\ 20x\ \sin\ \left(2x^2-3\right)$$  

• $$3-20x\ \sin\left(2x^2-3\right)$$   

• $$3\ -\ 20\ \sin\ \left(2x^2-3\right)$$  

• $$3\ +\ 20\ \sin\left(2x^2-3\right)$$  

Multiple Choice

Derive $$y\ =\ 4x\ \tan\ 6x.$$  

• $$4x\ \tan\ 6x\ +\ 24\ \sec^26x$$  

• $$4x\ \tan\ 6x\ +\ 24x\ \csc^26x$$  

• $$4\ \tan\ 6x\ +\ 24\ x\ \sec^26x$$  

• $$4\tan6x\ -\ 24x\ \csc^26x$$  

Multiple Choice

$$\frac{d}{dx}\left[\sin\left(2x\right)\right]$$  

• $$\cos\left(2x\right)$$  

• $$2\sin\left(2x\right)$$  

• $$2\cos\left(2x\right)$$  

Multiple Choice

$$\frac{d}{dx}\left[\sin\left(x^2+x\right)\right]$$  

• $$\left(2x+1\right)\cos\left(x^2+x\right)$$  

• $$\cos\left(2x+1\right)$$  

• $$\cos\left(x^2+x\right)$$  

Multiple Choice

$$\frac{d}{dx}\left[\sin x\cos x\right]$$  

• 1

• $$-\sin x\cos x$$  

• $$\cos^2x-\sin^2x$$  

Multiple Choice

Find the derivative of

$$g\left(x\right)=5x^4-3x^2+x-\cos\left(x\right)$$  

• $$f'\left(x\right)=5x^4-3x^2+x-\sin\left(x\right)$$  

• $$g'\left(x\right)=20x^3-6x+1+\sin\left(x\right)$$  

• $$g'\left(x\right)=20x^3-6x+1-\sin\left(x\right)$$  

• $$g'\left(x\right)=20x^3-6x+\sin\left(x\right)$$  

Multiple Choice

Find the derivative of

$$f\left(x\right)=\left(3x^2-2x\right)\sin\left(x\right)$$

• $$f'\left(x\right)=\left(6x-2\right)\cos\left(x\right)$$

• $$f'\left(x\right)=\left(3x^2-2x\right)\cos\left(x\right)+\left(6x-2\right)\sin\left(x\right)$$

• $$f'\left(x\right)=\left(3x^2-2x\right)\cos\left(x\right)$$

• $$f'\left(x\right)=\left(6x-2\right)\cos\left(x\right)+\left(3x^2-2x\right)\sin\left(x\right)$$

Antiderivatives and Indefinite Integration

By Sahel Otoom

Match

Warm up

Match the following

• $$\frac{d}{dx}\left(\sin7x\right)$$

• $$\frac{d}{dx}\left(\cot x^2\right)$$

• $$\frac{d}{dx}\left(-20e^{2x^{ }}\right)$$

• $$\frac{d}{dx}\left(2x+1\right)^n$$

• $$\frac{d}{dx}\left(\ln\ 77x\right)$$

7 cos 7x

-2x csc² x²

-40e^2x

2n(2x+1)^n-1

1/x

• 7 cos 7x

• -2x csc² x²

• -40e^2x

• 2n(2x+1)^n-1

• 1/x

Multiple Choice

∫ 4 dx

• 0

• 4t + C

• 4x + C

• 2x² + C

Multiple Choice

$$\int0dx$$  

• $$\frac{1}{x}+C$$  

• $$Not\ Possible$$  

• $$x+C$$  

• $$C$$  

Multiple Choice

∫ t⁶ dt

• 6t⁵

• 6t⁵ + C

• 1/7 t⁷ + C

• t⁷ + C

Multiple Choice

Find $$\int(2x+3)dx$$  

• $$x^2+3x+c$$  

• $$x^2+3x$$  

• $$2x^2+3x+c$$  

• $$2x^2+3$$  

Multiple Choice

Find $$\int(12x^3−4x)dx$$  

• $$3x^4-2x^2+c$$  

• $$3x^4-4x^2+c$$  

• $$4x^3-2x+c$$  

• $$12x^4-x^2+c$$  

Multiple Choice

Find $$\int(7−x^2)dx$$  

• $$7x−\frac{1}{3}x^3+c$$  

• $$7x−x^3+c$$  

• $$−\frac{1}{3}x^3+c$$  

• $$7−x^3+c$$  

Multiple Choice

Find $$\int(x^2+x+1)dx$$  

• $$x^3+x^2+x+c$$  

• $$\frac{1}{3}x^3+\frac{1}{2}x^2+x+c$$  

• $$\frac{1}{3}x^3+\frac{1}{2}x^2+x$$  

• $$x^3+x^2+x$$  

Multiple Choice

Find $$\int(x^4+5x^2)dx$$  

• $$\frac{1}{4}x^4+\frac{5}{2}x^3+c$$  

• $$\frac{1}{5}x^5+\frac{5}{3}x^3+c$$  

• $$\frac{1}{5}x^5+\frac{1}{3}x^3+c$$  

• $$5x^5+10x^3+c$$  

Multiple Choice

Find $$\int x(x^2−3)dx$$  

• $$\frac{1}{4}x^4−\frac{3}{2}x^2+c$$  

• $$\frac{1}{4}x^4−\frac{1}{2}x^2+c$$  

• $$\frac{x^2}{2}\left(\frac{x^3}{3}-3x\right)+c$$  

• $$\frac{x^2}{2}\left(\frac{x^3}{3}-3x\right)$$  

Multiple Choice

Find $$\int(x−2)^2dx$$  

• $$\frac{1}{3}x^3−2x^2+4x+c$$  

• $$\frac{x^2}{2}-2x+c$$  

• $$\frac{x^2}{2}-4x+c$$  

• $$\frac{1}{3}x^3−4x+c$$  

Multiple Choice

Find $$\int(3x^4+x^2−6)dx$$  

• $$15x^5+\frac{1}{3}x^3−6x+c$$  

• $$\frac{1}{5}x^5+\frac{1}{3}x^3−6x+c$$  

• $$\frac{3}{5}x^5+\frac{1}{3}x^3−6x+c$$  

• $$\frac{3}{5}x^5+\frac{1}{3}x^3−6+c$$  

Multiple Choice

Find $$\int(2+\frac{1}{x^2})dx$$  

• $$2x−x^{−1}+c$$  

• $$2−x^{-1}+c$$  

• $$2x-\frac{3}{x^3}+c$$  

• $$2x-\frac{1}{x^3}+c$$  

Multiple Choice

Find $$\int(x-\frac{1}{x^3})dx$$  

• $$\frac{1}{2}x^2+\frac{1}{2}x^{−2}+c$$  

• $$\frac{1}{2}x^2+\frac{1}{4}x^{−4}+c$$  

• $$\frac{1}{2}x^2-\frac{1}{2}x^{−2}+c$$  

• $$\frac{1}{2}x^2-\frac{1}{4}x^{−4}+c$$  

Multiple Choice

Which of the following is the indefinite integral of $$\frac{x^3}{2}+7$$ ?

• $$\frac{3x^2}{2}$$  

• $$\frac{3x^2}{2}+7x+c$$  

• $$\frac{x^4}{8}+7x+c$$  

• $$\frac{x^4}{8}+c$$  

Multiple Choice

Integrate $$\sqrt{x}$$ with respect to x

• $$x^{\frac{1}{2}}+c$$  

• $$\frac{1}{2}x^{-\frac{1}{2}}+\ c$$  

• $$\frac{2}{3}x^{\frac{3}{2}}+\ c$$  

• $$\frac{3}{2}x^{\frac{3}{2}}+\ c$$  

Multiple Choice

Which of the following is the indefinite integral of $$\frac{3}{x^4}\ \ ?$$

• $$-\frac{1}{x^3}+\ c$$  

• $$\frac{3}{5x^5}+\ c$$  

• $$-\frac{12}{x^5}+\ c$$  

• $$\frac{1}{x^3}+\ c$$  

Multiple Choice

$$\int5x^4dx$$  

• $$x^5$$  

• $$\frac{5}{4}x^5+C$$  

• $$x^5+C$$  

• $$20x^3$$  + C

Multiple Choice

$$\int6x\left(x+2\right)dx$$  

• $$6x^2+12x+C$$  

• $$x^{2\ }-2x+C$$  

• $$3x^2+6x+C$$  

• $$2x^3+6x^2+C$$

Multiple Choice

If y = $$ax^n$$  , then $$\int_{ }^{ }y\ dx\ =$$  

• $$\frac{ax^{n+1}}{n+1}$$  

• $$\frac{ax^{n-1}}{n-1}+\ c$$  

• $$\frac{ax^{n+1}}{n}+\ c$$  

• $$\frac{ax^{n+1}}{n+1}+\ c$$  

Multiple Choice

$$\int6x^4+3x^2+5x\ +5\ dx$$  

• $$5x^5+3x^4+5x^2\ +5x$$  

• $$5x^5+3x^3+5x^2\ +5x$$  

• $$\frac{6}{5}x^5+x^3+5x^2\ +5x\ +c$$  

• $$\frac{6}{5}x^5+x^3+\frac{5}{2}x^2\ +5x\ +c$$  

Multiple Choice

$$\int_{ }^{ }3x^2+4x\ dx$$  

• $$x^3+4x^2+c$$  

• $$x^3+2x^2+c$$  

• $$\frac{3}{2}x^3+4x^2+c$$  

• $$3x^3+4x^2+c$$  

Multiple Choice

What is the most general antiderivative of 

$$\cos\left(x\right)$$  ?

• $$-\sin\left(x\right)+c$$  

• $$\sin\left(x\right)$$  

• $$\sin\left(x\right)+c$$  

• $$-\sin\left(x\right)$$  

Multiple Choice

What is the derivative of   $$\tan\left(x\right)$$  ?

• $$\cot\left(x\right)$$  

• $$\sec\left(x\right)\tan\left(x\right)$$  

• $$\sec^2\left(x\right)$$  

• $$-\csc\left(x\right)\cot\left(x\right)$$  

Multiple Choice

• -sec x + C
• sec x + C
• tan x + C
• tan² x + C

Multiple Choice

• cos x + C
• tan x + C
• -cos x + C
• -tan x + C

Multiple Choice

• -csc x + C
• csc x + C
• -tan x + C
• tan x + C

Multiple Choice

• csc x + C
• -csc x + C
• -cot x + C
• tan x + C

Multiple Choice

• cot x + C
• cos x + C
• -cso x + C
• -cot x + C

Multiple Choice

• sin x + C
• tan x + C
• sin² x + C
• -sin x + C

Multiple Choice

∫ sin (2x) dx

• cos(2x)+C
• -(1/2)cos(2x)+C
• -cos(2x)+C
• (1/2)cos(2x)+C

Multiple Choice

∫ 4sec²(2x) dx

• 2tan(x) + c

• 4tan(2x) + c

• 4tan(2x)

• 2tan(2x) + c

Multiple Choice

Evaluate the indefinite integral.

$$\int\left(2e^x+\sec x\tan x-\sqrt{x}\right)\ dx$$  

• $$2e^x+\sec x-\frac{2}{3}x^{\frac{3}{2}}+C$$  

• $$e^x+\sec x-\frac{1}{2}x^{\frac{1}{2}}+C$$  

• $$e^{2x}+\csc x-\frac{2}{3}x^{\frac{3}{2}}+C$$  

• $$2e^x+\cot x-\frac{1}{2}x^{\frac{1}{2}}+C$$  

Multiple Choice

Evaluate the indefinite integral.

$$\int\left(3x^4-2x^{-3}+\sec^2x\right)\ dx$$  

• $$\frac{3}{5}x^5+\frac{1}{2}x^{-4}+\cot x+C$$  

• $$\frac{3}{5}x^5+\frac{1}{2}x^{-4}+\tan x+C$$  

• $$15x^5+x^{-2}+\tan x+C$$  

• $$\frac{3}{5}x^5+x^{-2}+\tan x+C$$  

Multiple Choice

Evaluate the indefinite integral.

$$\int4\sec^2x\ dx$$  

• $$4\tan x+C$$  

• $$4\cos x+C$$  

• $$4\csc x+C$$  

• $$4\cot x+C$$  

Multiple Choice

Evaluate the indefinite integral.

$$\int_{ }^{ }5\csc^2x\ dx$$  

• $$-5\cot x+C$$  

• $$-5\tan x+C$$  

• $$-5\csc x+C$$  

• $$-5\sin x+C$$  

Multiple Choice

Evaluate the indefinite integral.

• A

• B

• C

• D

Multiple Choice

$$\int\left(4x^3-3x^2-2\right)dx\ ,\ and\ \ find\ C\ \ if\ f\left(2\right)=5$$  

• $$12x^2-6x$$  

• $$x^4-x^3-2x\ +c$$  

• $$x^4-x^3-2x+5$$  

• $$x^4-x^3-2x+1$$  

Multiple Choice

Given g(x) = x + 2 and G(0) = 3, find G(x).

• 1/2 x² + 2x + 3

• 1/2 x² + 2x + 6

• x² + 3

• x² + 2x + 6

Multiple Choice

$$\int\left(4x^3-3x^2-2\right)dx\ ,\ and\ \ find\ C\ \ if\ f\left(2\right)=5$$  

• $$12x^2-6x$$  

• $$x^4-x^3-2x\ +c$$  

• $$x^4-x^3-2x+5$$  

• $$x^4-x^3-2x+1$$  

Match

Match the following

• $$\ln\left|x\right|+C$$

• $$-\frac{1}{x}+C$$

• $$e^x+C$$

• $$x+C$$

• $$\frac{2}{3}\sqrt[]{x^3}+C$$

• $$\int_{ }^{ }\frac{1}{x}dx\$$

• $$\int_{ }^{ }\frac{1}{x^2}dx$$

• $$\int_{ }^{ }e^xdx$$

• $$\int_{ }^{ }1dx$$

• $$\int_{ }^{ }\sqrt[]{x}dx$$

Multiple Choice

$$f'(x)=$$   $$2x^2+4x\ +3$$  Find f(x), when f(0) = 5

• $$\frac{2}{3}x^3+2x^2+3x\$$  

• $$\frac{2}{3}x^3+2x^2\ +3x\ +5$$  

• $$\frac{2}{3}x^3+2x\ ^2+3x\$$  

• $$4x\ +4$$  

Multiple Choice

$$Find\ f\left(x\right)=\int\left(6x^5+12x^3+\frac{1}{2}x\right)\ dx\ \ \ \ \ if\ f\left(1\right)=2$$  

• $$30x^4+\frac{9}{4}x^2\ +c$$  

• $$x^6+3x^4+x^2$$  

• $$x^6+3x^4+x^2-3$$  

• $$x^6+3x^4+x^2+5$$  

Multiple Choice

∫25sec²x dx

• 25 secx tanx + C
• 25 tanx + C
• -25 tanx + C
• -25 sec x + C