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Mathematics
Mathematics
Problem
Determine the exact volume of the solid generated when the region bounded by
y
=
sin
x
y=\sin x
y
=
sin
x
and
y
=
cos
x
y=\cos x
y
=
cos
x
on
0
≤
x
≤
π
2
0\le x\le \dfrac{\pi}{2}
0
≤
x
≤
2
π
is revolved about the horizontal line
y
=
−
1
y=-1
y
=
−
1
. a)
π
(
2
2
−
3
2
)
\pi\bigl(2\sqrt{2}-\dfrac{3}{2}\bigr)
π
(
2
2
−
2
3
)
b)
π
(
4
2
−
3
)
\pi\bigl(4\sqrt{2}-3\bigr)
π
(
4
2
−
3
)
c)
π
(
2
2
−
2
)
\pi\bigl(2\sqrt{2}-2\bigr)
π
(
2
2
−
2
)
d)
π
(
4
2
−
3
2
)
\pi\bigl(4\sqrt{2}-\dfrac{3}{2}\bigr)
π
(
4
2
−
2
3
)
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