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Joint Entrance Examination
Mathematics
Area Under Curves
Question 173
Question 173 of 230
Medium
MCQ
The area enclosed by the curves
y
2
+
4
x
=
4
y^2+4x=4
y
2
+
4
x
=
4
and
y
−
2
x
=
2
y-2x=2
y
−
2
x
=
2
is:
A
25
/
3
25/3
25/3
B
22
/
3
22/3
22/3
C
9
D
23
/
3
23/3
23/3
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Official solution
Required area
=
∫
−
4
2
(
4
−
y
2
4
−
y
−
2
2
)
d
y
=\int_{-4}^{2}\left(\frac{4-y^{2}}{4}-\frac{y-2}{2}\right) d y
=
∫
−
4
2
(
4
4
−
y
2
−
2
y
−
2
)
d
y
=
∫
−
4
2
8
−
2
y
−
y
2
4
d
y
=\int_{-4}^{2} \frac{8-2 y-y^{2}}{4} d y
=
∫
−
4
2
4
8
−
2
y
−
y
2
d
y
=
1
4
{
8
y
−
y
2
−
y
3
3
}
−
4
2
=\frac{1}{4}\left\{8 y-y^{2}-\frac{y^{3}}{3}\right\}_{-4}^{2}
=
4
1
{
8
y
−
y
2
−
3
y
3
}
−
4
2
=
9
=9
=
9
square units
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