Evaluate: (i) `intsin^2x\ dx` (ii) `intcos^2x\ dx` (iii) `intsin^2xcos^2x dx`

Explanation

(i)
`text { Let } I=int sin ^{2} x {dx} `

`therefore 1=int frac{1-cos 2 x}{2} {dx} `

`therefore I=frac{1}{2}[int 1 d x-int cos 2 x d x] `

`therefore I=frac{1}{2}[x-frac{sin 2 x}{2}]+C `

`therefore I=frac{x}{2}-frac{sin 2 x}{4}+C`


(ii)
Recall the identity `cos 2 x=2 cos ^{2} x-1,`

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