Question

Using integration, find the area bounded by the curve y² = 4ax and the line x = a.

Answer 1

Given: y² = 4ax

Required area (A) = `2int_0^ay.dx`

= `2int_0^a sqrt(4ax).dx`

= `4sqrt(a) int_0^a  sqrt(x)  dx`

= `4sqrt(a)[x^(3//2)/(3/2)]_0^a`

= `8/3sqrt(a)[a^(3//2) - 0]`

= `8/3a^(1/2 + 3/2)`

= `8/3a^(4/2)`

= `8/3a^2` sq.units.