1
You visited us
1
times! Enjoying our articles?
Unlock Full Access!
Byju's Answer
Other
Quantitative Aptitude
Functions
Draw a rough ...
Question
Draw a rough sketch of the curve,
y
=
x
2
+
3
x
+
2
x
2
−
3
x
+
2
and find the area of the bounded region between the curve and x-axis.
Open in App
Solution
f
(
x
)
=
(
x
+
1
)
(
x
+
2
)
(
x
−
1
)
(
x
−
2
)
Graph will cut x-axis at
x
=
−
1
and
x
=
−
2
It is discontinuous at
x
=
1
and
x
=
2
.
lim
x
→
∞
f
(
x
)
→
1
,
lim
x
→
1
−
f
(
x
)
→
+
∞
lim
x
→
1
+
f
(
x
)
→
−
∞
lim
x
→
2
−
f
(
x
)
→
−
∞
lim
x
→
2
+
f
(
x
)
→
+
∞
,
f
(
0
)
=
1
.
Now we have to find the area of the shaded region. The required area
=
∣
∣
∣
∫
−
1
−
2
f
(
x
)
d
x
∣
∣
∣
=
∣
∣
∣
∫
−
1
−
2
(
x
2
+
3
x
+
2
x
2
−
3
x
+
2
)
d
x
∣
∣
∣
=
∣
∣
∣
∫
−
1
−
2
1
+
6
x
(
x
−
1
)
(
x
−
2
)
d
x
∣
∣
∣
=
∣
∣ ∣
∣
[
x
∣
∣
−
1
−
2
+
6
∫
−
1
−
2
(
2
x
−
2
−
1
x
−
1
)
d
x
]
∣
∣ ∣
∣
=
∣
∣
[
1
+
6
[
2
l
n
|
x
−
2
|
−
l
n
|
x
−
1
|
]
−
1
−
2
∣
∣
=
∣
∣
1
+
6
[
2
(
l
n
3
−
l
n
4
)
−
(
l
n
2
−
l
n
3
)
]
∣
∣
=
∣
∣
1
+
6
[
3
l
n
3
−
5
l
n
2
]
∣
∣
=
6
l
n
(
32
27
)
−
1
sq. units.
Suggest Corrections
0
Similar questions
Q.
Draw a rough sketch of the curve and find the area of the region bounded by curve
y
2
=
8
x
and the line
x
=
2
.
Q.
Draw a rough sketch to indicate the region bounded between the curve y
2
= 4x and the line x = 3. Also, find the area of this region.