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find the area bounded between the curve y x2 and y
Question:
Find the area bounded between the curve
y
=
x
2
and
y
=
x
3
.
MHT CET
Updated On:
Mar 29, 2024
(A)
1
2
(B)
1
12
(C)
1
(D)
1
24
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The Correct Option is
B
Solution and Explanation
Explanation:
Given:
y
=
x
3
and
y
=
x
2
Finding a point of intersection:
⇒
x
3
−
x
2
=
0
⇒
x
2
(
x
−
1
)
=
0
⇒
x
=
0
,
1
Let us draw the graph of the curve
y
=
x
2
and
y
=
x
3
Let the required area be A.Using the formula of the area under the curve,
A
=
|
∫
a
b
f
(
x
)
−
g
(
x
)
dx
|
⇒
A
=
|
∫
0
1
(
x
3
−
x
2
)
dx
|
=
|
[
x
4
4
−
x
3
3
]
0
1
|
Substitute the limit to evaluate the area:
⇒
A
=
|
1
4
−
1
3
−
0
+
0
|
=
1
12
Hence, the correct option is (B).
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