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

`(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 ENGLISH|Exercise Single Correct Answer Type|30 Videos

  • AREA

    CENGAGE ENGLISH|Exercise Multiple Correct Answer Type|3 Videos

  • AREA

    CENGAGE ENGLISH|Exercise Numerical Value Type|18 Videos

  • APPLICATIONS OF DERIVATIVES

    CENGAGE ENGLISH|Exercise Comprehension Type|5 Videos

  • BINOMIAL THEOREM

    CENGAGE ENGLISH|Exercise Matrix|4 Videos

Similar Questions

Explore conceptually related problems

The area (in square units) of the region bounded by y^(2)=2x and y=4x-1 , is

The area (in sq. units) of the region {(x,y):y^(2) le 2x and x^(2)+y^(2) le 4x , x ge 0, y le 0}, is

The area (in sq. units) of the region {(x,y):y^(2) le 2x and x^(2)+y^(2) le 4x , x ge 0, y le 0}, is

The area (in sq units) of the region A={(x,y):(y^(2))/(2) le x le y+4} is

The area (in sq units) of the region A={(x,y): x^(2) le y le x +2} is

The area (in sq units) of the region A={(x,y): x^(2) le y le x +2} is

The area (in sq. units) of the region bounded by the curves y=2-x^(2) and y=|x| is k, then the value of 3k is

The area (in sq. units) of the region bounded by the curves y=2^(x) and y=|x+1| , in the first quadrant 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 (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