Free Printable Assessment SM025 Week 2 (Miss jade)

1.

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

a)

$\frac{ax^{n+1}}{n+1}$

b)

$\frac{ax^{n-1}}{n-1}+\ c$

c)

$\frac{ax^{n+1}}{n}+\ c$

d)

$\frac{ax^{n+1}}{n+1}+\ c$

2.

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

a)

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

b)

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

c)

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

d)

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

3.

Integrate $\int\left(2x+1\right)^{10}\ dx$ with respect to x.

a)

$22\left(2x+1\right)^{11}+c$

b)

$\frac{1}{22}\left(2x+1\right)^{11}+c$

c)

$11\left(2x+1\right)^{10}+c$

d)

$\frac{1}{11}\left(2x+1\right)^{10}+c$

4.

$\int_{ }^{ }\ \frac{1}{x}+\ \frac{1}{x^2}\ dx$

a)

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

b)

$x^0\ -\ x^{-1}+\ c$

c)

$\ln x+\ x^{-1}+\ c$

d)

$\ln x-\ x^{-1}+\ c$

5.

Integrate $\sin\left(\frac{x}{2}\right)$ with respect to x

a)

$\cos\left(\frac{x}{2}\right)\ +\ c$

b)

$-2\cos\left(\frac{x}{2}\right)\ +\ c$

c)

$-\cos\left(\frac{x}{2}\right)\ +\ c$

d)

$-\frac{1}{2}\cos\left(\frac{x}{2}\right)\ +\ c$

6.

$\int_{ }^{ }\sec^2\ 5x\ \ dx\ \ =$

a)

$\tan\ x\ \ +\ c$

b)

$\frac{1}{5}\tan\ x\ \ +\ c$

c)

$\frac{1}{5}\tan\ 5x\ \ +\ c$

d)

$\frac{1}{5}\tan^2\ 5x\ \ +\ c$

7.

Find the integral with respect to x of $\int_{ }^{ }\ \left(e^{3x}\right)^2\ dx\ .$

a)

$\frac{e^{6x}}{6}\ +\ c$

b)

$\frac{e^{9x}}{9}\ +\ c$

c)

$6e^{6x}\ +\ c$

d)

$\left(e^{3x}\right)^2\ +\ c$

8.

Find indefinite integral for $\int_{ }^{ }\frac{1}{e^{5x}}\ dx$

a)

$\frac{1}{5}e^{5x}\ +\ c$

b)

$-5e^{4x}\ +\ c$

c)

$\frac{e^{-5x}}{-5}+\ c$

d)

$\frac{e^{-4x}}{-4}+\ c$

9.

∫ 6 x (x² +1 )² dx

a)

( x² + 1)³ + C

b)

3 ( x² + 1)³ + C

c)

( x² + 1)¹ + C

d)

6 ( x² + 1)³ + C

10.

∫ 2x cos(x²) dx

a)

sin(x²) + C

b)

2 sin ( 2x ) + C

c)

(1/2) sin(x²) + C

d)

4 cos(2x ) + C

11.

a)

ln(2x²+6) + C

b)

ln(2x²+6)(4x) + C

c)

1/(2x²+6) + C

d)

1/(2x²+6)²+ C

12.

∫ x (x² + 7 )^(1/3) dx

a)

(3/4) ( x²+ 7 )^(4/3) + C

b)

(3/8) ( x²+ 7 )^(4/3) + C

c)

( x²+ 7 )^(4/3) + C

d)

(3/2) ( x²+ 7 )^(4/3) + C

13.

∫ g ' ( x ) f (u) dx, u = g ( x )

a)

∫ f ( u ) du

b)

g ( x ) + C

c)

( 1/ g ( x ) ) g ( x)⁴ + C

d)

cannot be determined

14.

What is the choice of u for ∫ e^x(1+e^x)^(1/2) dx?

a)

e^x

b)

1+e^x

c)

(1+e^x)^(1/2)

d)

(e^x)^(1/2)

15.

What is the Integration by Parts Formula?

a)

b)

c)

d)

16.

Evaluate the indefinite integral using integration by parts. u and v ' are provided.
$\int t\sin t\ dt\ ;\ \ \ u=t,\ v\ '=\sin t\$

a)

$t\cos^{-1}t-\left(1-t^2\right)^{\frac{1}{2}}+C$

b)

$-t\cos t+\sin t+C$

c)

$t\sin^{-1}t+\left(1-t^2\right)^{\frac{1}{2}}+C$

d)

$t\sin t+\cos t+C$

17.

a)

A

b)

B

c)

C

d)

D

18.

What would you choose for your u here if you used integration by parts?

a)

t

b)

3t

c)

e^2t

d)

e^t

e)

don't use IBP, let u = 2t

19.

Determine $\int_{ }^{ }x\ \sin2x\ dx$

a)

$\frac{-x\ \sin2x}{2}+\frac{\cos2x}{4}+c$

b)

$\frac{-x\ \cos2x}{4}+\frac{\sin2x}{2}+c$

c)

$\frac{-x\ \cos2x}{2}+\frac{\sin2x}{4}+c$

d)

$-x\ \sin2x+\cos2x+c$

20.

Evaluate the indefinite integral using integration by parts.
$\int t\cdot2^t\ dt\ ;\ \ \$

a)

$\frac{t^2\ln2t^2-t^2}{2}+C$

b)

$\frac{t\cdot2^t}{\ln2}-\frac{2^t}{\left(\ln2\right)^2}+C$

c)

$\frac{t^3\ln t}{3}-\frac{t^3}{9}+C$

d)

$\frac{2t^{\frac{3}{2}}\ln2t}{3}-\frac{4t^{\frac{3}{2}}}{9}+C$

21.

What is the solution of following :(please leave your answer in small letter)

(a)

Assessment SM025 Week 2 (Miss jade)

Total questions: 21

Worksheet time: 37mins

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