Question

Find the area of the region bounded by the curve y = x² and the line y = 4.

Answer 1

Required area (A) = 2 × Area of OPQO

= `2 xx int_0^4 x . dy`

= `2  int_0^4 sqrt(y)  . dy`

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

= `2 xx 2/3 xx 4^(3/2)`

= `2 xx 2/3 xx 8`

A = `32/3` sq. units.