The area (in sq. units) of the region (x,y)∈R2:x2≤y≤3-2x is:

x2≤y⇒(x,y) lies above y=x2 and y≤3-2x means (x,y) lies below 2x+y=3 Point of intersection of y=x2&y=-2x+3 is obtained by x2+2x-3=0⇒x=-3,1 So, Area =∫-313-2x-x2dx=3(4)-212-322-13+333=12+8-283=323