Question

Find out the area of the shaded region in the enclosed figure.

Answer 1

The curve is x² = y

We have to find area between y = 0 and y = 4

∴ We have to find the area of BNO.

Area of BNO = `int_0^4 x  dy`

We know that x² = y

Taking the square root on both sides:

x = `±sqrty`

Since BNO is in 1^st quadrant.

We take the positive value of x.

∴ x = `sqrty`

Area of BCFE = `int_0^4 x  dy`

= `int_0^4 sqrt(y)  dy`

= `int_0^4 (y)^(1/2) dy`

= `[y^(3/2)/(3/2)]_0^4`

= `2/3 [y^(3/2)]_2^4`

= `2/3[(4)^(3/2) - (0)^(3/2)]`

= `2/3 [(4)^(3/2)]`

= `2/3 [2^2 xx 3/2]`

= `2/3 xx 2^3`

= `(2 xx 8)/3`

= `16/3` sq. units