The area(in sq. units) of the region x,y∈R2|4x2≤y≤8x+12 is _____

We have 4x2=y⇒y=8x+12⇒4x2=8x+12⇒x2−x−3=0⇒x2−2x−3=0⇒x2−3x+x−3=0⇒x+1x-3=0⇒x=−1,3∴Area=A=∫−138x+12−4x2dx                  =8x22+12x−4x33−13 =49+36−36−4−12+43 =36+8−43                   =44−43=132−43=1283