Integration Learning Quizzes for Applied Mathematics Certificate in Engineering

Question 1

Calculate the integral of sin(2x) cos(2x) dx.

Accepted Answer

-1/2 cos(4x) + C

Answer

1/2 sin(4x) + C

Answer

sin(2x) cos(2x) + C

Answer

-sin(4x) + C

Question 2

What is the integral of x^2 with respect to x?

Accepted Answer

x^3/3 + C

Answer

x^3 + C

Answer

3x^2 + C

Answer

x^2 + C

Question 3

What is the integral of sin(x) with respect to x?

Accepted Answer

-cos(x) + C

Answer

cos(x) + C

Answer

-sin(x) + C

Answer

sin(x) + C

Question 4

What is the integral of e^x with respect to x?

Accepted Answer

e^x + C

Answer

e^x - C

Answer

ln(e^x) + C

Answer

ln(e^x - C)

Question 5

What is the indefinite integral of ∫ cos(x) dx?

Accepted Answer

sin(x) + C

Answer

cos(x) + C

Answer

sec(x) + C

Answer

csc(x) + C

Question 6

Find the integral of 1/(x^2 + 1). **The integral of 1/(x^2 + 1) is arctan(x) + C, where C is the constant of integration.**

Accepted Answer

arctan(x) + C

Answer

tan^(-1)(x) + C

Answer

cot^(-1)(x) + C

Answer

arccot(x) + C

Question 7

Find the integral of the function f(x) = e^x. **The integral of e^x is e^x + C, where C is the constant of integration.**

Accepted Answer

e^x + C

Answer

e^x

Answer

x*e^x

Answer

x*e^x + C

Question 8

Find the integral of ∫x^2 dx with respect to x.

Accepted Answer

x^3/3 + C

Answer

2x + C

Answer

x + C

Answer

x^2 + C

Question 9

Find the integral of ∫(x^2 + 2x - 1) dx.

Accepted Answer

x^3/3 + x^2 - x + C

Answer

2x^3 + x^2 - x + C

Answer

x^3 - x^2 + x + C

Answer

x^2 + 2x - 1 + C

Question 10

Calculate the integral of ∫(1 / x) dx.

Accepted Answer

ln(|x|) + C

Answer

1 / x + C

Answer

x^2 / 2 + C

Answer

x / 2 + C

Question 11

Integrate ∫e^x dx.

Accepted Answer

e^x + C

Answer

x * e^x + C

Answer

1 / e^x + C

Answer

e^x/x + C

Question 12

∫cos(2x) dx is equal to:

Accepted Answer

1/2 sin(2x) + C

Answer

cos(2x) / 2 + C

Answer

2 sin(2x) + C

Answer

-sin(2x) / 2 + C

Question 13

Find the integral of x^2 + 2x - 1 with respect to x.

Accepted Answer

(x^3)/3 + x^2 - x + C

Answer

(x^2)/2 + 2x + C

Answer

2x^3 + x^2 - C

Answer

(x^3)/2 - x + C

Question 14

Which substitution would you use to integrate ∫(2x + 1)^3 dx?

Accepted Answer

u = 2x + 1

Answer

u = 1

Answer

u = 2x

Answer

u = x^2

Question 15

Find the indefinite integral of ∫x * e^x dx.

Accepted Answer

x * e^x - e^x + C

Answer

e^x + C

Answer

e^x - x * e^x + C

Answer

(x^2)/2 * e^x + C

Question 16

Find the indefinite integral of 1 / (x^2 + 1).

Accepted Answer

arctan(x) + C

Answer

1 / (x^2 + 1) + C

Answer

x / (x^2 + 1) + C

Answer

ln(x^2 + 1) + C

Question 17

Find the area under the curve y = x^2 between x = 0 and x = 2.

Accepted Answer

(8 / 3)

Answer

4

Answer

(4 / 3)

Answer

8

Question 18

What is the integral of the expression  'x² + 2x' with respect to x?

Accepted Answer

x³/3 + x² + C

Answer

2x² + 2x + C

Answer

x³ + 2x + C

Answer

x²/2 + 2x² + C

Question 19

What is the integral of e^x with respect to x?

Accepted Answer

e^x + C

Answer

-e^x + C

Answer

-1/e^x + C

Answer

1/e^x + C

Question 20

What is the integral of ln(x) with respect to x?

Accepted Answer

x*ln(x) - x + C

Answer

1/x*ln(x) + C

Answer

x*ln(x) + x + C

Question 21

What is the integral of 1/(x² + 1) with respect to x?

Accepted Answer

arctan(x) + C

Answer

1/x² + C

Answer

-1/x² + C

Answer

-arctan(x) + C