`intsin^(3)xdx` का मान ज्ञात कीजिए ।

Options

A. `-(3)/(4)cosx+(1)/(2)cos3x+c`
B. `-(3)/(4)cosx+(1)/(12)cos3x+c`
C. `-(1)/(4)cosx+(1)/(12)cos3x+c`
D. `(3)/(4)cosx+(1)/(12)cos3x+c`

Answer

B

Explanation

हम जानते हैं की `sin3x=3sinx-4sin^(3)x`
`rArr" "sin^(3)x=(3sinx-sin3x)/(4)`
`therefore intsin^(3)xdx=int(3sinx-sin3x)/(4)dx`
`=(3)/(4)intsinxdx-(1)/(4)int sin 3x dx`
`=-(3)/(4)cosx-(1)/(4).(1)/(3)(-cos3x)+c`
`=-(3)/(4)cosx+(1)/(12)cos3x+c`