Let f(x) = ∫ x^3 √(3-x^2) dx. If 5f (√2) = -4, then f(1) is equal to

Question

Let f(x) = \(\int x^3 \sqrt{3-x^2} \ dx.\) If \(5f(\sqrt2) = -4, \) then f(1) is equal to

(1) \(-\frac{2\sqrt2}{5}\) 

(2) \(-\frac{6\sqrt2}{5}\) 

(3) \(-\frac{4\sqrt3}{5}\) 

(4) \(-\frac{8\sqrt2}{5}\)

Answer 1

Correct option is: (2) \(-\frac{6\sqrt2}{5}\)  

Let \(3 - x^2 = y^2\) 

\(\therefore -x\ dx=ydy\)   

\(\therefore \ xdx=-ydy\)