Evaluate Definite Integrals - 1 PDF

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Kuta Software - Infinite Calculus

Name___________________________________

Fundamental Theorem of Calculus

Date________________ Period____

Evaluate each definite integral. 1)



3

(−x 3 + 3 x 2 + 1 ) dx



2)

−1

1

(x 4 + x 3 − 4x 2 + 6) dx −2

f(x)

−8

3)

5)





−6

−4

f(x)

8

8

6

6

4

4

2

2

−2

2

4

6

8 x

−8

−6

−6

−8

−8

4)

0

−1

2

−4

1

(x

−2

−4

(2x 2 − 12 x + 13) dx

− 4 x + 4x + 4 ) dx 3

−4

−2

3

5

−6

−2

6)





3

(−x 3 + 3 x 2 − 2) dx 0

0

1 3 4 x dx

−3

4

6

8 x

−1

7)



−4



13)

15)



10) 2cos x dx

−

11)

8)

π 6

−

9)

−1

4 − 3 dx x







−3

4 dx x



2



2

1

2

dx

2

x −1

x

π 4

−2

1

12)

5( 2x + 4) 3 dx −3

1 2x − 2

e

14)

dx

−1

3

f (x) dx, f (x ) = 0

{

x − 1, 2 2

x≤2

x − 6x + 8, x > 2

16)





−1

2

(2x + 4) 3

dx

−2

(−x +

−3 x − 9

−4

1 2

− x + 4x dx −5

) dx

Kuta Software - Infinite Calculus

Name___________________________________

Fundamental Theorem of Calculus

Date________________ Period____

Evaluate each definite integral. 1)



3

(−x 3 + 3 x 2 + 1 ) dx

2)

−1



1

(x 4 + x 3 − 4x 2 + 6) dx −2

f(x)

−8

−6

−4

f(x)

8

8

6

6

4

4

2

2

−2

2

4

6

8 x

−8

−6



5)

−4

−6

−6

−8

−8



177 = 8.85 20

( 2x 2 − 12x + 13) dx

4)

1



0 5

− 4 x + 4x + 4 ) dx 3

−1

17 ≈ 2.833 6

3

(−x 3 + 3 x 2 − 2) dx 0

3 = 0.75 4

14 ≈ −4.667 3

(x

2

−4

3

−

−2 −2

12

3)

−4

−2

6)



0

1 3 4 x dx

−3 3

−9 3 ≈ −12.98

4

6

8 x

−1

7)



−1

4 − 3 dx x

−4

8)



−4 ln 3 ≈ −4.394

15 = 1.875 8

π 6

−

9)



10) 2cos x dx

−



1

12)

5( 2x + 4) 3 dx −3



3

13)



1

e

dx

14)

−1

e4 − 1 ≈ 0.491 2e 4

15)



3

f (x) dx, f (x ) = 0

5 − ≈ −1.667 3

2

dx

2

x −1

x

2

−1

2

(2x + 4) 3

dx

15 ≈ 0.117 128

15 2 ≈ −4.725 − 4

2x − 2

1

π ≈ 0.262 12

2 ≈ 0.414

−2

2



π 4

−1 +

11)

−3

4 dx x



−2

(−x +

−3 x − 9

) dx

−4

9

{

x − 1, x≤2 2 x 2 − 6x + 8, x > 2

16)



1 2

− x + 4x dx −5

−

46 ≈ −15.333 3

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