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calculate the area under the curve y 2x and includ
Question:
Calculate the area under the curve
y
=
2
x
and included between the lines
x
=
0
,
x
=
4
.
MHT CET
Updated On:
Jun 23, 2024
(A)
32
5
(B)
32
3
(C)
31
2
(D)
3
2
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The Correct Option is
B
Solution and Explanation
Explanation:
Given here,
y
=
2
x
∴
y
2
=
4
x
(
x
≥
0
)
We need to determine area under curve
y
2
=
4
x
(
x
≥
0
)
included between the lines
x
=
0
,
x
=
4
as:
So, the area under curve will be given as:
=
∫
0
4
2
x
dx
=
2
∫
0
4
x
1
2
dx
We know that:
∫
x
n
d
x
=
x
n
+
1
n
+
1
x
m
+
n
=
(
x
m
)
(
x
n
)
Therefore,
2
∫
0
4
x
1
2
dx
=
2
[
x
1
+
1
2
1
+
(
1
2
)
]
0
4
=
2
[
x
1
+
(
1
2
)
3
2
]
0
4
=
2
[
2
3
(
(
4
)
1
+
(
1
2
)
−
0
)
]
=
2
[
2
3
(
(
4
)
1
(
4
)
1
2
)
]
=
(
2
)
(
2
)
(
4
)
(
2
)
3
=
32
3
sq unitsHence, the correct option is (B).
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