Prove that begin mathsize 20px style integral e to the power of 2 x end exponent sin x cos x d x equals 1 over 8 e to the power of 2 x end exponent open parentheses sin 2 x minus cos 2 x close parentheses plus c end style

Asked by sunil2791 | 26th May, 2017, 01:04: PM

Expert Answer:

begin mathsize 16px style straight I equals integral straight e to the power of 2 straight x end exponent sinxcosxdx
straight I equals 1 half integral 2 straight e to the power of 2 straight x end exponent sinxcosxdx
straight I equals 1 half integral straight e to the power of 2 straight x end exponent sin 2 xdx
Put space 2 straight x equals straight t
dx equals dt over 2
straight I equals 1 fourth integral straight e to the power of straight t sintdt
Using space integration space by space parts space solve space it space further.
we space will space appreciate space if space you space solve space it space and space post space it space to space us. end style

Answered by Sneha shidid | 26th May, 2017, 04:49: PM

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