Question

Find the area of the region lying in the first quandrant bounded by the curve y²= 4x, X axis and the lines x = 1, x = 4

Answer 1

Let A be the required area
Consider the equation, y² = 4x

∴ 1y=2sqrtx`

∴ `A=int_1^4ydx`

`=int_1^4 2sqrtxdx`

`=2.2/3[x^(3/2)]_1^4`

`=4/3[(4)^(3/2)-(1)^(3/2)]`

`=4/3[8-1]`

`A=28/3` sq.units