80 Part I: The Questions
553. f x
t dt
x
( )
sin ( )
= ∫
2
1
1
554. f x
t t
dt
x
( ) =
+
∫
1
4
1
3
555. f x
t
dt
x
x
( ) tan
=
+
∫
1
3
3
556. f x
t
t
dt
x
x
( ) =
−
+
∫
2
4
2
6
1
1
557. f x
dt
t
x
x
( ) log
= ∫ 5
5
2
Working with Basic Examples
of Definite Integrals
558–570 Evaluate the definite integral using basic
antiderivative rules.
558.
5
1
3 dx
∫
559.
cos x dx
0
4
π
∫
Using the Fundamental
Theorem of Calculus to
Find Derivatives
546–557 Find the derivative of the given function.
546. f x
t dt
x
( ) =
+
∫ 1 4
0
547. f x
t
dt
x
( ) =
+
(
)
∫ 2
6
4
3
548. f x
t
t dt
x
( )
cos( )
= ∫
3
0
549. f x
e dt
t
x
( ) = ∫
2
4
550. f x
t dt
x
( ) sin
=
−
( )
∫ 1
2
0
551. f x
e dt
t
x
( ) ln
=
+
( )
∫ 2 1
4
552. f x
t
t dt
x
( )
sin
cos
=
+
(
)
∫
2
1