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Question
Mathematics
The area enclosed between the curve y2(2a-x)=x3 and the line x = 2 above the x-axis is
Q. The area enclosed between the curve
y
2
(
2
a
−
x
)
=
x
3
and the line
x
=
2
above the
x
-axis is
1607
205
Application of Integrals
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A
π
a
2
sq. units
18%
B
2
3
π
a
2
sq. units
45%
C
2
π
a
2
sq. units
27%
D
3
π
a
2
sq. units
9%
Solution:
The required area
A
=
0
∫
2
a
2
a
−
x
x
3
d
x
put
x
=
2
a
s
i
n
2
θ
⇒
d
x
=
2
a
2
s
in
θ
cos
θ
d
θ
⇒
A
=
8
a
2
0
∫
π
(
2
1
−
cos
2
θ
)
2
d
θ
=
2
a
2
0
∫
π
(
1
−
2
cos
2
θ
+
co
s
2
2
θ
)
d
θ
=
2
a
2
0
∫
π
(
1
−
2
cos
2
θ
+
2
1
+
cos
4
θ
)
d
θ
=
2
3
π
a
2