∫ (√sin x) cos x dx = ?

Question

Mark (√) against the correct answer of the following:

\(\int(\sqrt{sin\,x})cos\,x\,dx=?\)

∫ (√sin x) cos x dx = ?

A. \(\frac{2}{3}(cos\, x)^{3/2} + C\)

B. \(\frac{3}{2}(cos\, x)^{3/2} + C\)

C. \(\frac{2}{3}(sin\, x)^{3/2} + C\)

D. \(\frac{3}{2}(sin\, x)^{3/2} + C\)

Answer 1

Correct answer is C.

Given = \(\int(\sqrt{sin\,x})cos\,x\)

∫ (√sin x) cos x dx

Let, sin x = z²

⇒ cos x dx = 2 z dz

So,

where c is the integrating constant.