If \int \sqrt{x} (1-x^3) ^{\frac{-1}{2}} \dx=\frac{2}{3} g(f(x))+c, then

Correct Answer is : f(x)=x32,g(x)=sin−1x

f(x)=\sqrt{x}, g(x)= \sin ^{-1} x

f(x)=x^{\frac{3}{2}}, g(x)= \sin ^{-1} x

f(x)=x^{\frac{3}{2}}, g(x)=\cos ^{-1} x

f(x)=\sqrt{x}, g(x)=\cos ^{-1} {\x}

AP EAPCET 18th May 2023 Shift 1 Solved Paper

Section: Mathematics

Question : 71 of 160

Marks: +1, -0

If ∫√x(1−x3)‌

−1

‌dx=‌

g(f(x))+c, then

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