InterviewSolution
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InterviewSolution
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निम्न फलनों के मान ज्ञात कीजिये - `int_(0)^(pi//4)sin 3x cosx dx` |
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Answer» 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)` |
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