Exercises
UF Calculus Set 30
1. Find the general antiderivative for each function below; assume we have chosen an interval
I
on which the function is continuous. Several will require an algebraic manipulation ﬁrst.
(a)
f
(
x
) = 4
x
5
(b)
f
(
x
) =
π
√
10 +
ex
(c)
f
(
x
) =
8
9
x
2
/
3
(d)
f
(
x
) = 2
x
+ 2
x

2
(e)
f
(
x
) = 4 sin(
x
) + 2 cos(2
x
)
(f)
f
(
x
) = sec
2
(
πx
)
(g)
f
(
x
) =
e

2
x
+
e
2
x
(h)
f
(
x
) =
(1 +
√
x
)
2
x
(i)
f
(
x
) =
x

1
/
3
(6

x
)
(j)
f
(
x
) = (1

2
x
2
)
2
(k)
f
(
x
) =
4

x
2

√
x
(l)
f
(
x
) =
x
2

1
1 +
x
2
2. Find the particular antiderivative
F
for
f
(
x
)
satisfying the conditions, and write the largest
open interval on which
F
is the antiderivative for
f
(a)
f
(
x
) = 2
x
+ 2
x

2
;
F
passes through
(
1
2
,
4 )
(b)
f
(
x
) =
x

1
/
3
(6

x
)
;
F
(

1) = 5
(c)
f
(
x
) =
e

2
x
+
e
2
x

sec(
x
) tan(
x
)
;
F
(0) = 0
3. Use trigonometric identities to manipulate the functions below in order to ﬁnd the general
antiderivative.
(a)
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 Spring '08
 ALL
 Calculus, Algebra, Geometry, Derivative, 1 mile, 20 ft, 15 days, 32 ft

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