1 $What is the indefinite integral of a constant with respect to ?$

A.

B.

C.

$0$

D.

2 $Evaluate .$

A.

B.

C.

D.

3 $What does the 'C' represent in an indefinite integral?$

A.

The area under the curve

B.

The derivative of the function

C.

The constant of integration

D.

The upper limit of integration

4 $Calculate .$

A.

B.

C.

D.

5 $Evaluate .$

A.

B.

C.

D.

6 $What is ?$

A.

B.

C.

D.

7 $What is ?$

A.

B.

C.

D.

8 $Evaluate .$

A.

B.

C.

D.

9 $Find .$

A.

B.

C.

D.

10 $Evaluate .$

A.

B.

C.

D.

11 $What property allows us to write ?$

A.

Power Rule

B.

Sum Rule

C.

Product Rule

D.

Chain Rule

12 $Evaluate .$

A.

B.

C.

D.

13 $If is the antiderivative of, then is equal to:$

A.

B.

C.

D.

14 $Evaluate the definite integral .$

A.

6

B.

8

C.

12

D.

24

15 $What is the value of ?$

A.

B.

Infinite

C.

D.

16 $If and, what is ?$

A.

6

B.

14

C.

-6

D.

2

17 $Evaluate .$

A.

$1$

B.

C.

D.

18 $Which relation is true regarding switching the limits of integration?$

A.

B.

C.

D.

19 $Evaluate .$

A.

B.

1

C.

2

D.

20 $If is an odd function, then equals:$

A.

B.

$0$

C.

D.

Infinite

21 $Calculate .$

A.

B.

C.

$0.5$

D.

$1$

22 $What is the primary purpose of Integration by Substitution?$

A.

To integrate products of functions

B.

To reverse the Chain Rule

C.

To find the area between two curves

D.

To integrate rational functions

23 $To solve, which substitution is best?$

A.

B.

C.

D.

24 $Solve using substitution.$

A.

B.

C.

D.

25 $Evaluate .$

A.

B.

C.

D.

26 $Determine .$

A.

B.

C.

D.

27 $Solve .$

A.

B.

C.

D.

28 $Which of the following requires Integration by Parts?$

A.

B.

C.

D.

29 $What is the formula for Integration by Parts?$

A.

B.

C.

D.

30 $In the LIATE rule for choosing 'u' in integration by parts, what does 'L' stand for?$

A.

Linear

B.

Logarithmic

C.

Limit

D.

Long

31 $Apply integration by parts to . If, what is ?$

A.

B.

C.

D.

32 $Using integration by parts on, the result is:$

A.

B.

C.

D.

33 $To integrate using parts, we choose and . What is ?$

A.

$1$

B.

C.

D.

34 $What is the result of ?$

A.

B.

C.

D.

35 $Evaluate using substitution.$

A.

B.

C.

D.

36 $The geometric interpretation of for is:$

A.

The slope of the tangent line

B.

The length of the curve

C.

The area under the curve from to

D.

The volume of rotation

37 $Find the area under the curve from to .$

A.

4

B.

8

C.

16

D.

32

38 $Calculate the area under between and .$

A.

3

B.

9

C.

18

D.

27

39 $Find the area under the constant line from to .$

A.

5

B.

25

C.

30

D.

6

40 $Find the area under from to .$

A.

B.

$1$

C.

D.

41 $What is the area under the curve from to ?$

A.

B.

1

C.

D.

Infinite

42 $Evaluate to find the area under the cosine curve.$

A.

B.

1

C.

D.

43 $If calculating the area between a curve and the x-axis, and the curve dips below the x-axis, the integral result for that section is:$

A.

Positive

B.

Negative

C.

Zero

D.

Undefined

44 $Find the area bounded by, the x-axis, and .$

A.

3

B.

6

C.

9

D.

12

45 $Evaluate .$

A.

B.

C.

D.

46 $What is ?$

A.

B.

C.

D.

47 $When changing variables in a definite integral using substitution, what must happen to the limits of integration?$

A.

They remain the same

B.

They must be transformed to and

C.

They become 0 and 1

D.

They switch places

48 $Integration is often described as the reverse process of:$

A.

Multiplication

B.

Differentiation

C.

Exponentiation

D.

Factorization

49 $Find .$

A.

B.

C.

$2$

D.

50 $Which rule helps solve ?$

A.

Substitution Rule

B.

Power Rule

C.

Integration by Parts (applied twice)

D.

Sum Rule

Unit 5 - Practice Quiz