363
Answers
501–600
Answers and Explanations
565.
45
2
Rewrite the radical using exponential notation:
2
2
3
1
8
1 3
1
8
xdx
x dx
∫
∫
=
Then use elementary antiderivative formulas:
2
2 4 3
2 3
4
3
2
3
2
8
1 3
1
8
4 3
1
8
4 3
1
8
4 3
1
8
4 3
x dx
x
x
x
∫
=








=






= ( )
=
−1 1
3
2
16 1
45
2
4 3
(
)
=
−
=
(
)
566.
1 4
− π
Using elementary antiderivative formulas gives you
csc
( cot
)
cot
c ot
2
4
2
4
2
1
2 2
4 4
0
x
dx
x x
−
(
) = −
−
= −
−
(
) − − −
(
)
= −
∫ π
π
π
π
π
π
π π
π
2 2
1 4
1 4
− − −
( )
= −
π
π
567.
–10
Using elementary antiderivative formulas gives you
1 2
4
2
2
4 4
2 2 2
3
0
2
2
4
0
2
2
4
0
2
2
4
+ −
(
) = + −






= + −
(
)
= + −
(
) −
∫
y
y dy
y
y
y
y y
y
0 0 0 0
2 4 16
10
2
4
+ −
(
)
= + −
= −