` sqrt(sin 2x) cos 2x`

Options

A. `(1)/(3)(sinx)^(3//2)+C`
B. `(1)/(3)(sin x)^(1//2)+C`
C. `(1)/(3)(sin 2x)^(3//2)+C`
D. `(1)/(3)(sin 2x)^(1//2)+C`

Answer

C

Explanation

`intsqrt(sin2x)cos 2xdx`
Let `" "sin2x=t" "rArr" "2cos 2x=(dt)/(dx)`
`rArr" "dx=(dt)/(2cos 2x)`
`therefore int sqrt(sin2x)cos 2x dx=intsqrtt cos 2x(dt)/(2cos 2x)=(1)/(2)int sqrtt dt`
`=(1)/(2)(t^(1//2+1))/(((1)/(2)+1))+C=(1)/(3)t^(3//2)+C`
`=(1)/(3)(sin2x)^(3//2)+C`