Home
Class 12
MATHS
The area (in sq. units) of the region...

The area (in sq. units) of the region described by `{(x ,""y)"":""y^2lt=2x` and `ygeq4x-1}` is : (1) `7/(32)` (2) `5/(64)` (3) `(15)/(64)` (4) `9/(32)`

A

`(7)/(32)`

B

`(5)/(64)`

C

`(15)/(64)`

D

`(9)/(32)`

Text Solution

Verified by Experts

The correct Answer is:
D
`y^(2)le2x` represents the interior of parabola `y^(2)=2x` (towards focus) and `yge4x-1` represents the half region of plane to the left of the line `y=4x-1`.

`overset(1)underset(-1//2)int((y+1)/(4)-(y^(2))/(2))dy=(1)/(4){(y^(2))/(2)+y}_(-1//2)^(1)-(1)/(6){y^(3)}_(-1//2)^(1)`
`=(1)/(4){((1)/(2)+1)-((1)/(8)-(1)/(2))}-(1)/(6){1+(1)/(8)}`
`=(1)/(4){(3)/(2)+(3)/(8)}-(1)/(6){(9)/(8)}=(15)/(32)-(6)/(32)=(9)/(32)`
Promotional Banner

Topper's Solved these Questions

  • AREA

    CENGAGE|Exercise JEE Advanced Previous Year|9 Videos

  • AREA

    CENGAGE|Exercise Single Correct Answer Type|27 Videos

  • AREA

    CENGAGE|Exercise Exercise (Numerical)|16 Videos

  • APPLICATIONS OF DERIVATIVES

    CENGAGE|Exercise Subjective Type|2 Videos

  • AREA UNDER CURVES

    CENGAGE|Exercise Question Bank|10 Videos

Similar Questions

Explore conceptually related problems

The area (in sq units) of the region {(x, y) : y^2 gt= 2x and x^2 + y^2 lt= 4x, x gt= 0, y gt= 0} is

The area (in sq. units) of the region A=[(x,y):0leylexabsx+1" and "-1lexlex] is

The area (in sq. units) bounded by the curves y=x (x-3)^2 and y=x is

The area (in sq units) of the region bounded by the curve y = sqrtx and the lines y = 0, y = x - 2, is

The area (in sq. units) of the region bounded by the parabola y=x^2+2" and the lines " y=x+1, x=0 " and " x=3 , is

The area of the region bounded by x^(2)+y^(2)-2x-3=0 and y=|x|+1 is

Find the area of the region bounded by the parabolas y^2=4x and x^2=4y .

Find the area of the region bounded between y^2=4x and x^2=4y .