Home
Class 12
MATHS
Find the area of the region bounded by ...

Find the area of the region bounded by the curve `y^2= x`and the lines `x = 1, x = 4`and the x-axis.

Text Solution

Verified by Experts

`y^(2)=x` is a symmetric curve about X-axis. ABCDA is the region bounded by `x=1, x=4` and `y^(2)=x` and X-axis.

Required area `=` area of ABCDA
`=int_(1)^(4)|y|dx=int_(1)^(4)sqrt(x)dx`
`=[(x^(3//2))/(3//2)]_(1)^(4)=(2)/(3)[4^(3//2)-1^(3//2)]`
`=(2)/(3)(8-1)=(14)/(3)` sq. units.
Promotional Banner

Topper's Solved these Questions

  • APPLICATIONS OF INTEGRALS

    NAGEEN PRAKASHAN|Exercise Exercise 8.2|7 Videos

  • APPLICATIONS OF INTEGRALS

    NAGEEN PRAKASHAN|Exercise Miscellaneous Exercise|19 Videos

  • APPLICATIONS OF INTEGRALS

    NAGEEN PRAKASHAN|Exercise Exercise 8 C Questions For Competitive Examinations|10 Videos

  • APPLICATIONS OF DERIVATIVES

    NAGEEN PRAKASHAN|Exercise Miscellaneous Exercise|24 Videos

  • Continuity and Differentiability

    NAGEEN PRAKASHAN|Exercise Miscellaneous Exercise|23 Videos

Similar Questions

Explore conceptually related problems

Find the area of the region bounded by the curve y^(2)=4x and the line x=3

Find the area of the region bounded by the curve y=x^(2) and the line y=4

Find the area of the region bounded by the curve y =x ^(2) and the line y =4.

Find the area of the region bounded by the curve xy=1 and the lines y=x,y=0,x=e

Find the area of the region bounded by the curve (y-1)^2=4(x+1) and the line y= x-1

The area of the region bounded by the curve y = x ^(2) and the line y =16 is :

The area bounded by the curve y^(2) = 14x and the lines x = 1, x = 4 above X-axis is

The area of the region bounded by the curves y = | x – 2 l, x = 1, x = 3 and the x-axis is

Find the area of the region bounded by the curve y^(2)=4x" and " x^(2)=4y .

Find the area of the region bounded by the curve y^(2)=4x" and " x^(2)=4y .

Knowledge Check

  • The area of the region bounded by the curve y = x ^(2) and the line y =16 is :

    A
    `32/3`
    B
    `(256)/(3)`
    C
    `(64)/(3)`
    D
    `(128)/(3)`

  • The area bounded by the curve y^(2) = 14x and the lines x = 1, x = 4 above X-axis is

    A
    `7/3 sq. units`
    B
    `14/3 sq. units`
    C
    `28/3 sq. units`
    D
    `56/3 sq. units`

  • The area of the region bounded by the curves y = | x – 2 l, x = 1, x = 3 and the x-axis is

    A
    3
    B
    2
    C
    1
    D
    4