area of bounded regions

Question : Find Area of the loop of the curve ay^2=x^2(a-x) Solution: Given curve \[ay^2=x^2\left(a-x\right)\] (1) Substituting y=0 into above equation \[0=x^2\left(a-x\right)\] x=0, a From eqn (1) \[y=\pm\frac{x}{\sqrt a}\sqrt{x-a}\] So…