MATH260—Week 6 Lab
Name:
Samuel Swapp
Antiderivatives
According to the first part of the fundamental theorem of calculus, the antiderivative reverses the
derivative.
If f(x) is a derivative, F(x) is the antiderivative.
Directions:
Look at the examples below and answer questions 1 and 2.
Let f(x) be a derivative and F(x) be the antiderivative.
a.)
f(x) = 3x
2
F
(
x
)=
3
x
2
+
1
2
+
1
=
x
3
b.)
f(x) = 5x – 6
F
(
x
)=
5
x
1
+
1
1
+
1
−
6
x
0
+
1
1
=
5
2
x
2
−
6
x
c.)
f
(
x
)=
3
√
x
−
1
x
4
F
(
x
)=
x
1
3
+
3
3
4
3
−
x
−
4
+
1
−
3
=
3
4
x
4
3
+
1
3
x
3
.

2) Find the antiderivative of f(x) = 3x
5
+ x – 4. Show all work.

3) How is an antiderivative related to a derivative? How can that relationship help you to check
your antiderivatives and integrals answers?

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4) What do the derivatives of the following antiderivatives
have in common?
F(x) = 3x
2
+ 5
,
G(x) = 3x
2
+ 9
,
H(x) = 3x
2
– 11

Indefinite Integrals:
∫
f
(
x
)
dx
=
F
(
x
)+
C
Used for finding the general form of the antiderivative.

Directions:
Look at the examples, then find each of the integrals below.
C
x