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Lesson Example Discussion Quiz: Class Homework

Quiz At Home

Title: Integration

Grade: 1400-a Lesson: S2-L6

Explanation: Hello Students, time to practice and review. Let us take next 10-15 minutes to solve the ten problems using the Quiz Sheet. Then submit the quiz to get the score. This is a good exercise to check your understanding of the concepts.

Quiz: at Home

Problem Id	Problem	Options
1	Evaluate the definite integral: \$ \int_0^2 (3x^2 + 2x + 1)dx\$	A) 12 B) 14 C) 16 D) 18
2	If \$f(x) = (A sin(pix))/2 + B\$, \$f^(-1) (1/2) = \sqrt(2)\$ and \$\int_0^1 f(x) dx = (2A)/(pi)\$, then the constants A and B are respectively.	A) \$A = pi\$ and B= 0 B) \$A = 4/pi\$ and B= 0 C) A = 4 and B = 0 D) \$A = pi/4\$ and B= 0
3	If \$\int (sec^2 x - 2010)/ (sin^(2010) x)\$ dx = \$(p(x))/ (sin^(2010) x) + c\$, then value of \$p(pi/3)\$ is?	A) \$-1/\sqrt(3)\$ B) \$1/\sqrt(3)\$ C) \$-\sqrt(3)\$ D) \$\sqrt(3)\$
4	Let f(x) be the maximum and g(x) be the minimum of \$x\|x\|, x^2\|x\|\$ then \$\int_-1^1 (f(x) - g(x))\$ dx = ?	A) \$1/3\$ B) \$7/12\$ C) \$1/12\$ D) \$2/3\$
5	The value of \$\int_(-(pi)/2)^((pi)/2) ((cos x) / (1 + e^x)) dx\$ is?	A) 2 B) 3 C) 1 D) \$pi\$
6	Solve the integral: \$ \int (sin^5x/cos^3x) dx \$.	A) \$ (1/2)sec^4x + 2 ln \|cosx\| - (1/2)cos^4 x + C \$ B) \$ (1/2)sec^2x + 4 ln\|cosx\| - (1/2)cos^2 x + C \$ C) \$ (1/2)sec^2x + 2 ln\|cosx\| - (1/2)cos^2 x + C \$ D) \$ (1/4)sec^2x + 2 ln\|cosx\| - (1/2)cos^2 x + C \$
7	Evaluate the integral: \$ \int xln(x) dx \$.	A) \$ ((x^2)/2 ln(x)) - (x^2/4) + C \$ B) \$ ((x^2)/4 ln(x)) - (x^2/4) + C \$ C) \$ ((x^2)/2 ln(x)) - (x^2/6) + C \$ D) \$ 2((x^2)/2 ln(x)) - (x^2/6) + C \$
8	Evaluate the integral: \$ \int_0^(pi/2) cos^2(x) dx \$	A) \$ pi/4 \$ B) \$ pi/2 \$ C) \$ pi/6 \$ D) \$ pi/8 \$
9	Evaluate the integral: \$ \int (dx/(\sqrt(4 − x^2))) \$.	A) \$ arctan(x/4) + C \$ B) \$ arcsin(x/2) + C \$ C) \$ arcsin(x/6) + C \$ D) \$ arctan(x/2) + C \$
10	\$ \int ((18x - 17)/((2x - 3)(x + 1))) dx \$ =	A) \$ 7 ln \∣2x − 3\∣ + 2 ln\∣x + 1\∣ + C \$ B) \$ 2 ln\∣2x − 3\∣ + 7 ln\∣x + 1\∣ + C \$ C) \$ 8 ln\∣2x − 3\∣ + 7 ln\∣x + 1\∣ + C \$ D) \$ 4 ln\∣2x − 3\∣ + 7 ln\∣x + 1\∣ + C \$

Problem Id

Problem

Options

Evaluate the definite integral:

\$ \int_0^2 (3x^2 + 2x + 1)dx\$

A) 12

B) 14

C) 16

D) 18

If \$f(x) = (A sin(pix))/2 + B\$, \$f^(-1) (1/2) = \sqrt(2)\$ and \$\int_0^1 f(x) dx = (2A)/(pi)\$, then the constants A and B are respectively.

A) \$A = pi\$ and B= 0

B) \$A = 4/pi\$ and B= 0

C) A = 4 and B = 0

D) \$A = pi/4\$ and B= 0

If \$\int (sec^2 x - 2010)/ (sin^(2010) x)\$ dx = \$(p(x))/ (sin^(2010) x) + c\$, then value of \$p(pi/3)\$ is?

A) \$-1/\sqrt(3)\$

B) \$1/\sqrt(3)\$

C) \$-\sqrt(3)\$

D) \$\sqrt(3)\$

Let f(x) be the maximum and g(x) be the minimum of \$x|x|, x^2|x|\$ then \$\int_-1^1 (f(x) - g(x))\$ dx = ?

A) \$1/3\$

B) \$7/12\$

C) \$1/12\$

D) \$2/3\$

The value of \$\int_(-(pi)/2)^((pi)/2) ((cos x) / (1 + e^x)) dx\$ is?

A) 2

B) 3

C) 1

D) \$pi\$

Solve the integral: \$ \int (sin^5x/cos^3x) dx \$.

A) \$ (1/2)sec^4x + 2 ln |cosx| - (1/2)cos^4 x + C \$

B) \$ (1/2)sec^2x + 4 ln|cosx| - (1/2)cos^2 x + C \$

C) \$ (1/2)sec^2x + 2 ln|cosx| - (1/2)cos^2 x + C \$

D) \$ (1/4)sec^2x + 2 ln|cosx| - (1/2)cos^2 x + C \$

Evaluate the integral: \$ \int xln(x) dx \$.

A) \$ ((x^2)/2 ln(x)) - (x^2/4) + C \$

B) \$ ((x^2)/4 ln(x)) - (x^2/4) + C \$

C) \$ ((x^2)/2 ln(x)) - (x^2/6) + C \$

D) \$ 2((x^2)/2 ln(x)) - (x^2/6) + C \$

Evaluate the integral: \$ \int_0^(pi/2) cos^2(x) dx \$

A) \$ pi/4 \$

B) \$ pi/2 \$

C) \$ pi/6 \$

D) \$ pi/8 \$

Evaluate the integral: \$ \int (dx/(\sqrt(4 − x^2))) \$.

A) \$ arctan(x/4) + C \$

B) \$ arcsin(x/2) + C \$

C) \$ arcsin(x/6) + C \$

D) \$ arctan(x/2) + C \$

\$ \int ((18x - 17)/((2x - 3)(x + 1))) dx \$ =

A) \$ 7 ln \∣2x − 3\∣ + 2 ln\∣x + 1\∣ + C \$

B) \$ 2 ln\∣2x − 3\∣ + 7 ln\∣x + 1\∣ + C \$

C) \$ 8 ln\∣2x − 3\∣ + 7 ln\∣x + 1\∣ + C \$

D) \$ 4 ln\∣2x − 3\∣ + 7 ln\∣x + 1\∣ + C \$