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Mathematics
Mathematics
Problem
Let
r
>
0
r>0
r
>
0
. Determine the exact area of the region lying above the
x
x
x
-axis and between
x
=
r
2
x = \dfrac{r}{2}
x
=
2
r
and
x
=
r
x = r
x
=
r
for the circle
x
2
+
y
2
=
r
2
x^{2}+y^{2}=r^{2}
x
2
+
y
2
=
r
2
. a)
r
2
(
π
6
+
3
8
)
r^{2}\left( \dfrac{\pi}{6} + \dfrac{\sqrt{3}}{8} \right)
r
2
(
6
π
+
8
3
)
b)
π
r
2
4
\dfrac{\pi r^{2}}{4}
4
π
r
2
c)
r
2
(
π
6
−
3
8
)
r^{2}\left( \dfrac{\pi}{6} - \dfrac{\sqrt{3}}{8} \right)
r
2
(
6
π
−
8
3
)
d)
r
2
(
π
3
−
3
8
)
r^{2}\left( \dfrac{\pi}{3} - \dfrac{\sqrt{3}}{8} \right)
r
2
(
3
π
−
8
3
)
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