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Question
Mathematics
If the area of the region bounded by the curves y 2-2 y=-x, x+y=0 is A, then 8 A is equal to
Q. If the area of the region bounded by the curves
y
2
−
2
y
=
−
x
,
x
+
y
=
0
is
A
, then
8
A
is equal to _________
148
135
JEE Main
JEE Main 2023
Application of Integrals
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Answer:
36
Solution:
y
2
−
2
y
=
−
x
⇒
y
2
−
2
y
+
1
=
−
x
+
1
(
y
−
1
)
2
=
−
(
x
−
1
)
y
=
−
x
Points of intersection
x
2
+
2
x
=
−
x
x
2
+
3
x
=
0
x
=
0
,
−
3
A
=
0
∫
3
(
−
y
2
+
2
y
+
y
)
d
y
=
2
3
y
2
−
3
y
3
∣
∣
0
3
=
2
9
8
A
=
36