निम्न फलनों के मान ज्ञात कीजिये –
`int_(0)^(pi//4)sin 3x cosx dx`
`int_(0)^(pi//4)sin 3x cosx dx`
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माना `I=int_(0)^(pi//4)sin 3x cos x dx`
`=(1)/(2)int_(0)^(pi//4)(2sin 3x cos x)dx`
`=(1)/(2)int_(0)^(pi/4)[sin 4x+sin 2x]dx`
`” “[because 2sin A cos B=sin (A+B)+sin(A-B)]`
`=(1)/(2)[-(cos4x)/(4)-(cos 2x)/(2)]_(0)^(pi//4)`
`=-(1)/(2)[(cos 4x)/(4)+(cos2x)/(2)]_(0)^(pi//4)`
`=-(1)/(2)[((cospi)/(4)+(cospi//2)/(2))-((cos0)/(4)+(cos0)/(2))]`
`=-(1)/(2)[(-(1)/(4)+0)-((1)/(4)+(1)/(2))]`
`=-(1)/(2)[-(1)/(4)-(1)/(4)-(1)/(2)]=(1)/(2)`