Home
Class 12
MATHS
Find the area bounded by the curve x^(2)...

Find the area bounded by the curve `x^(2)=y,x^(2)=-y, and y^(2)=4x-3.`

Text Solution

Verified by Experts

The correct Answer is:
`(1)/(3)` sq unit
The region bounded by the curves `y=x^(2), y = - x^(2) and y^(2)=4x-3` is symmetrical about X-axis, where `y=4x-3` is symmetrical about X-axis, where `y=4x-3` meets at (1, 1).
`therefore` Area of curve (OABCO)
`=2[int_(0)^(1) x^(2)dx - int_(3//4)^(1) (sqrt(4x-3)) dx]`

`=2[((x^(2))/(3))_(0)^(1)-(((4x-3)^(3//2))/(3*4//2))_(3//4)^(1)]`
`=2((1)/(3)-(1)/(6))`
`=1*(1)/(6)=(1)/(3)` sq unit
Promotional Banner

Similar Questions

Explore conceptually related problems

Find the area bounded by the curve x^2=y ,x^2=-ya n dy^2=4x-3

Find the area bounded by the curve x=7 -6y-y^2 .

Find the area bounded by the curve xy^(2)=4(2-x) and y-axis.

Find the area bounded by the curves y=x^(3)-x and y=x^(2)+x.

Find the area bounded by the curves (x -1)^(2) + y^(2) = 1 and x^(2) + y^(2) = 1 .

Find the area bounded by the curves x^2+y^2=4, x^2=-sqrt2 y and x=y

Find the area enclosed by the curves x^2=y , y=x+2

Find the area bounded by the curves x+2|y|=1 and x=0 .

Find the area bounded by x=2y-y^2