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

The area (in sq. units) of the region described by `{x,y):y^(2)le2x and yge4x-1}` is

A

A. `(7)/(32)`

B

B. `(5)/(64)`

C

C. `(15)/(64)`

D

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 PUBLICATION|Exercise Single Correct Answer Type|30 Videos

  • AREA

    CENGAGE PUBLICATION|Exercise Multiple Correct Answer Type|3 Videos

  • AREA

    CENGAGE PUBLICATION|Exercise Numerical Value Type|18 Videos

  • APPLICATIONS OF DERIVATIVES

    CENGAGE PUBLICATION|Exercise Subjective Type|2 Videos

  • BINOMIAL THEOREM

    CENGAGE PUBLICATION|Exercise Comprehension|11 Videos

Similar Questions

Explore conceptually related problems

The area of the region described by A={(x,y):x^(2)+y^(2)le1" and "y^(2)le1-x} 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 (A) 15/4 (B) 15/2 (C) 21/2 (D) 17/4

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 of the region described by A = {(x,y) : x^2 + y^2 lt= 1and y^2 lt= 1- x} is

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

The area (in square unit) of the region bounded by the curves y=x^(3) and y=2x^(2) 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 square unit ) of the region bounded by the line y= |x-1| and y=3- |x| is -

The area (in square unit ) of the region bounded by the curve x^(2)= 4y , the line x=2 and x- axis is -