Question

sketch the region bounded by the parabola x=$y^{2}$ and the line x=6-y and find the area of the region

Answer 1

Area=∫2−1ydx∫-12ydx

=∫2−1((x+2)−(x2))dx∫-12((x+2)-(x2))dx

=(x22+2x−x33)2−1(x22+2x-x33)-12

=(12(4−1)+2(2+1)−13(23+1))(12(4-1)+2(2+1)-13(23+1))

=32+6−332+6-3

=92