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Worksheet by Kuta Software LLC
Kuta Software - Infinite Calculus Name___________________________________
Period____Date________________
Fundamental Theorem of Calculus
Evaluate each definite integral.
1)
∫
−1
3
(
−
x
3
+ 3
x
2
+ 1
)
dx
x
f(x)
−8 −6 −4 −2 2 4 6 8
−8
−6
−4
−2
2
4
6
8
2)
∫
−2
1
(
x
4
+
x
3
− 4
x
2
+ 6
)
dx
x
f(x)
−8 −6 −4 −2 2 4 6 8
−8
−6
−4
−2
2
4
6
8
3)
∫
1
3
(
2
x
2
− 12
x + 13
)
dx 4)
∫
0
3
(
−
x
3
+ 3
x
2
− 2
)
dx
5)
∫
−1
0
(
x
5
− 4
x
3
+ 4
x + 4
)
dx
6)
∫
−3
0
4
x
1
3
dx
-1-
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Worksheet by Kuta Software LLC
7)
∫
−4
−1
−
4
x
3
dx 8)
∫
−3
−1
4
x
dx
9)
∫
−
π
4
−
π
6
2cos
x
dx
10)
∫
2
2
1
x
x
2
−
1
dx
11)
∫
−3
−2
5
(
2
x + 4
)
1
3
dx
12)
∫
−1
2
2
(
2
x + 4
)
3
dx
13)
∫
−1
1
e
2
x − 2
dx 14)
∫
−4
−2
(
−
x +
−3
x − 9
)
dx
15)
∫
0
3
f
(
x
)
dx,
f
(
x
)
=
{
x
2
− 1,
x ≤ 2
x
2
− 6
x + 8,
x > 2
16)
∫
−5
1
−
x
2
+
4
x
dx
-2-
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Worksheet by Kuta Software LLC
Kuta Software - Infinite Calculus Name___________________________________
Period____Date________________
Fundamental Theorem of Calculus
Evaluate each definite integral.
1)
∫
−1
3
(
−
x
3
+ 3
x
2
+ 1
)
dx
x
f(x)
−8 −6 −4 −2 2 4 6 8
−8
−6
−4
−2
2
4
6
8
12
2)
∫
−2
1
(
x
4
+
x
3
− 4
x
2
+ 6
)
dx
x
f(x)
−8 −6 −4 −2 2 4 6 8
−8
−6
−4
−2
2
4
6
8
177
20
= 8.85
3)
∫
1
3
(
2
x
2
− 12
x + 13
)
dx
−
14
3
≈ −4.667
4)
∫
0
3
(
−
x
3
+ 3
x
2
− 2
)
dx
3
4
= 0.75
5)
∫
−1
0
(
x
5
− 4
x
3
+ 4
x + 4
)
dx
17
6
≈ 2.833
6)
∫
−3
0
4
x
1
3
dx
−9
3
3 ≈ −12.98
-1-
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Worksheet by Kuta Software LLC
7)
∫
−4
−1
−
4
x
3
dx
15
8
= 1.875
8)
∫
−3
−1
4
x
dx
−4
ln 3 ≈ −4.394
9)
∫
−
π
4
−
π
6
2cos
x
dx
−1 + 2 ≈ 0.414
10)
∫
2
2
1
x
x
2
−
1
dx
π
12
≈ 0.262
11)
∫
−3
−2
5
(
2
x + 4
)
1
3
dx
−
15
3
2
4
≈ −4.725
12)
∫
−1
2
2
(
2
x + 4
)
3
dx
15
128
≈ 0.117
13)
∫
−1
1
e
2
x − 2
dx
e
4
− 1
2
e
4
≈ 0.491
14)
∫
−4
−2
(
−
x +
−3
x − 9
)
dx
9
15)
∫
0
3
f
(
x
)
dx,
f
(
x
)
=
{
x
2
− 1,
x ≤ 2
x
2
− 6
x + 8,
x > 2
−
5
3
≈ −1.667
16)
∫
−5
1
−
x
2
+
4
x
dx
−
46
3
≈ −15.333
-2-
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