Question

Find the area bounded by the curve y² = 36x, the line x = 2 in first quadrant 

Answer 1

Given equation of the curve is y² = 36x

∴ y = `+-  sqrt(36x)`

∴ y = `6sqrt(x)`     .....[∵ In first quadrant, y > 0]

Required area = `int_0^2 y  "d"x`

= `int_0^2 6sqrt(x)  "d"x`

= `6[(x^(3/2))/(3/2)]_0^2`

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

= `4(2sqrt(2))`

= `8sqrt(2)` sq.units