Free Printable G12A QZ. 5 Anti-Derivatives

1.

∫ x(x² - 4) dx

a)

x²/2(x³/3 - 4x) + C

b)

.25x⁴ -2x²+ C

c)

3x²- 4 + C

d)

x⁴ - 4x²+ C

2.

If f'(x) = 4x and f(1) = 6, then f(2) =

a)

6

b)

8

c)

9

d)

12

3.

Given v(t) = x^-9, determine the position function.

a)

(1/8)x^-8 + C

b)

(-1/8)x^-8+ C

c)

(1/10)x¹⁰

d)

(-1/8)x^-8

4.

FInd the antiderivative:
$f\left(x\right)=4x^3-2x+1$

a)

$12x^2-2+C$

b)

$x^4-x^2+C$

c)

$x^4-x^2+x+C$

d)

$12x-2+C$

e)

None of the above

5.

∫csc²x dx =

a)

-cotx + C

b)

cotx + C

c)

-tanx + C

d)

tanx + C

6.

∫secxtanx dx =

a)

secx + C

b)

-secx + C

c)

tanx + C

d)

-tanx + C

7.

Given v(t) = -sin(2x), determine the general for the antiderivative.

a)

cos(2x)

b)

2cos(2x)

c)

-cos(2x)

d)

1/2cos(2x)

8.

Find the anti-derivative:
$f\left(x\right)=\frac{1}{x^2+1}$

a)

$\ln\left(1+x^2\right)+C$

b)

$\frac{1}{2x}\ln\left(1+x^2\right)+C$

c)

$2x\tan^{-1}x+C$

d)

$\tan^{-1}x+C$

e)

None of the above

9.

Find the antiderivative of
(1/3)x³-5x

a)

(1/12)x⁴-(5/2)x²+C

b)

(1/4)x⁴-(1/2)x²+C

c)

(1/12)x³-(5)x²+C

d)

(12)x⁴-(5)x²+C

10.

Find the value of $f\left(x\right)$ if $f'\left(x\right)=4x^4-2x^2$ .

a)

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

b)

$f\left(x\right)=\frac{1}{5}x^5-\frac{1}{3}x^3+C$

c)

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

d)

$f\left(x\right)=16x^3-4x+C$

e)

$f\left(x\right)=5x^5-3x^3$

11.

If an object has an acceleration $a\left(t\right)=-2t^2+3t+1$ , then the displacement of the object is ...

a)

$s\left(t\right)=-\frac{1}{6}t^4+\frac{1}{2}t^3+\frac{1}{2}t^2+ct+d$

b)

$s\left(t\right)=\frac{1}{6}t^4+\frac{1}{2}t^3+\frac{1}{2}t^2+ct+d$

c)

$s\left(t\right)=-\frac{2}{3}t^4+\frac{1}{2}t^3+\frac{1}{2}t^2+ct+d$

d)

$s\left(t\right)=-\frac{1}{4}t^4+\frac{3}{2}t^3+\frac{1}{2}t^2+ct+d$

e)

$s\left(t\right)=\frac{3}{4}t^4-\frac{2}{3}t^3+\frac{1}{2}t^2+ct+d$

12.

The integration of f(x)= sin(x)/cos(x) dx is:

a)

- ln Icos(x)I + C

b)

ln Isin(x)I +C

c)

sec² (x) + C

d)

- ln Isin(x)I +C

13.

a)

-½x^-2 + C

b)

-⅖x^-5/2 + C

c)

2x^1/2 + C

d)

-2x^-1/2 + C

14.

Find

a)

b)

c)

d)

G12A QZ. 5 Anti-Derivatives

Total questions: 14

Worksheet time: 19mins

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