06 - Substitution for Definite Integrals - Kuta Software

Kuta Software - Infinite Calculus

Name___________________________________

Substitution for Definite Integrals

Date________________ Period____

Express each definite integral in terms of u, but do not evaluate. 1)

∫

0

∫

2

−1

3)

1

8x

(4 x

2

+ 1)

2

dx; u = 4 x + 1

2

∫ −12x (4x − 1) dx; u = 4x − 1 2

3

3

3

0

2

6 x( x − 1) dx; u = x − 1 2

2)

2

4)

−1

∫

1

∫

1

∫

1

24 x

(4 x

0

2

+ 4)

2

dx; u = 4 x 2 + 4

2

dx; u = 4 x 2 + 4

Evaluate each definite integral. 5)

∫

0

∫

0

−

−3

7)

8x

(2 x

2

+ 3)

2

2

dx; u = 2 x + 3

3

2

3

−1

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8)

0

16 x

(4 x

0

18 x (3 x + 3) dx; u = 3 x + 3 2

6)

2

+ 4)

8x

−

(4 x

2

+ 2)

2

dx; u = 4 x 2 + 2

Worksheet by Kuta Software LLC

Kuta Software - Infinite Calculus

Name___________________________________

Substitution for Definite Integrals

Date________________ Period____

Express each definite integral in terms of u, but do not evaluate. 1)

∫

0

−1

(4 x 1

∫

5

3)

∫

1

8x + 1)

2

1 u

2

dx; u = 4 x + 1

2

2)

∫ −12x (4x − 1) dx; u = 4x − 1 2

3

3

3

0

3

∫

du

2

3

−u du

−1

2 2

6 x( x − 1) dx; u = x − 1 2

2

4)

−1

∫

1

24 x

(4 x

0

3

∫ 3u du

8

∫

2

0

3 u

4

2

+ 4)

2

dx; u = 4 x 2 + 4

2

dx; u = 4 x 2 + 4

du

2

Evaluate each definite integral. 5)

∫

0

8x

−

(2 x

−3

2

+ 3)

2

2

dx; u = 2 x + 3

6)

∫

7)

∫

2

+ 4)

1 = 0.25 4

0 2

18 x (3 x + 3) dx; u = 3 x + 3 3

16 x

(4 x

0

4 ≈ 0.571 7

2

1

3

−1

8)

∫

1

8x

−

(4 x

0

18 −

2

+ 2)

2

dx; u = 4 x 2 + 2

1 ≈ −0.333 3

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Worksheet by Kuta Software LLC