Question

Find the area of the region enclosed by x = y^2 - 4y + 2 and x = y-2

Answer 1

$S=∫_1^4(y-2)dy -∫_1^4(y^2-4y+2)dy =∫_1^4(y-2) -(y^2-4y+2)dy=∫_1^4(y-2-y^2+4y-2)dy=∫_1^4(-y^2+5y-4)dy=(-y^3/3+5y^2/2-4y)|_1^4=-4^3/3+5*4^2/2-4*4-(-1^3/3+5*1^2/2-4*1)=-64/3+40-16-(-1/3+5/2-4)=-64/3+40-16+1/3-5/2+4=-21-3/2+28=7-2.5=4.5$