The area bounded by the curve 4y2=x2(4-x)(x-2) is equal to:

The given curve is 4y2=x2x−42−x2y=xx−42−x=x−x2+6x−8Area of the required region is AA=−2∫24x2−x2+6x−8dx=12∫246−2x−6−x2+6x−8dx=12∫246−2x−x2+6x−8dx−3∫241−x−32dx=1223−x2+6x−83224−3x−321−x−32−12sin−1x−324=130+30+sin−11=3π2