The area bounded by the curve a 2 y = x 2 ( x + a ) and the x -axis is

Step-by-step solution

The curve is y = x 2 ( x + a ) a 2 which is a cubic polynomial. Since x 2 ( x + a ) a 2 = 0 has a repeated root x = 0 , it touches x -axis at ( 0 ,   0 ) and intersects at ( - a ,   0 ) . Hence, required area = ∫ - a 0 y   d x = ∫ - a 0 x 2 x + a a 2 d x = 1 a 2 x 4 4 + a x 3 3 - a 0 = a 2 12   s q .   u n i t s