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Joint Entrance Examination
Mathematics
Area Under Curves
Question 24
Question 24 of 230
Medium
MCQ
The area (in sq. units) of the region
(
x
,
y
)
:
0
≤
y
≤
2
∣
x
∣
+
1
,
0
≤
y
≤
x
2
+
1
,
∣
x
∣
≤
3
{(x,y):0\le y\le 2|x|+1,0\le y\le {x}^{2}+1,|x|\le 3}
(
x
,
y
)
:
0
≤
y
≤
2∣
x
∣
+
1
,
0
≤
y
≤
x
2
+
1
,
∣
x
∣
≤
3
is
A
32
3
\frac{32}{3}
3
32
B
64
3
\frac{64}{3}
3
64
C
17
3
\frac{17}{3}
3
17
D
80
3
\frac{80}{3}
3
80
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Official solution
\[
Area
=
2
[
∫
0
2
(
x
2
+
1
)
d
x
+
∫
2
3
(
2
x
+
1
)
d
x
]
⇒
64
3
∴
(
2
)
\begin{aligned} & \text { Area }=2\left[\int_0^2\left(\mathrm{x}^2+1\right) \mathrm{dx}+\int_2^3(2 \mathrm{x}+1) \mathrm{dx}\right] \\ & \Rightarrow \frac{64}{3} \quad \therefore(2) \end{aligned}
Area
=
2
[
∫
0
2
(
x
2
+
1
)
dx
+
∫
2
3
(
2
x
+
1
)
dx
]
⇒
3
64
∴
(
2
)
\]
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