>
Exams
>
Mathematics
>
Straight lines
>
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
Hide Solution
Verified By Collegedunia
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).
Download Solution in PDF
Was this answer helpful?
0
0
Top Questions on Straight lines
If (1,5) is the midpoint of the segment of a line between the lines 5x −y −4 = 0 and 3x +4y −4=0,then the equation of the line will be:
WBJEE - 2024
Mathematics
Straight lines
View Solution
The perpendicular distance between two parallel lines \( 3x + 4y - 6 = 0 \) and \( 6x + 8y + 7 = 0 \) is equal to:
JEECUP - 2024
Mathematics
Straight lines
View Solution
Two straight lines \( 3x - 2y = 5 \) and \( 2x + ky + 7 = 0 \) are perpendicular to each other. The value of \( k \) is:
JEECUP - 2024
Mathematics
Straight lines
View Solution
If \( \left( 1 + \cos \frac{\pi}{8} \right) \left( 1 + \cos \frac{7\pi}{8} \right) \) =
KEAM - 2024
Mathematics
Straight lines
View Solution
\[ \cos^{-1} \left( \cos \left( \frac{-7\pi}{9} \right) \right) = \]
KEAM - 2024
Mathematics
Straight lines
View Solution
View More Questions
Questions Asked in MHT CET exam
A 2 kg object is in a gravitational field where the acceleration due to gravity is \( 9.8 \, \text{m/s}^2 \). What is the gravitational potential energy of the object at a height of \( 5 \, \text{m} \)?
MHT CET - 2025
work, energy and power
View Solution
A sound wave has a frequency of $ 440 \, \text{Hz} $. What is its time period?
MHT CET - 2025
Waves
View Solution
If \( \mathbf{a} = 2\hat{i} + 2\hat{j} + 3\hat{k}, \mathbf{b} = -\hat{i} + 2\hat{j} + \hat{k} \) and \( \mathbf{c} = 3\hat{i} + \hat{j} \) are the vectors such that \( \mathbf{a} + \lambda \mathbf{b} \) is perpendicular to \( \mathbf{c} \), then the value of \( \lambda \) is:
MHT CET - 2025
Vectors
View Solution
What is the empirical formula of a compound containing 40% sulfur and 60% oxygen by mass?
MHT CET - 2025
Chemical bonding and molecular structure
View Solution
A car accelerates uniformly from rest to a velocity of \( 25 \, \text{m/s} \) in \( 10 \, \text{seconds} \). What is the acceleration of the car?
MHT CET - 2025
Motion in a straight line
View Solution
View More Questions