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CBSE Class 12-science Answered

Integration e2x (1 – sin 2x/1 – cos 2x) dx explain in great detail
Asked by haroonrashidgkp | 28 Oct, 2018, 01:20: PM
answered-by-expert Expert Answer
begin mathsize 16px style straight I equals integral straight e to the power of 2 straight x end exponent open parentheses fraction numerator 1 minus sin 2 straight x over denominator 1 minus cos 2 straight x end fraction close parentheses dx
2 straight x equals straight t
straight x equals straight t over 2
dx equals dt over 2
straight I equals 1 half integral straight e to the power of straight t open parentheses fraction numerator 1 minus sint over denominator 1 minus cost end fraction close parentheses dt
straight I equals 1 half integral straight e to the power of straight t open parentheses fraction numerator 1 minus sint over denominator 2 sin squared begin display style straight t over 2 end style end fraction close parentheses dt
straight I equals 1 half integral straight e to the power of straight t open parentheses 1 half cosec squared straight t over 2 minus fraction numerator 2 sin begin display style straight t over 2 end style cos begin display style straight t over 2 end style over denominator 2 sin squared begin display style straight t over 2 end style end fraction close parentheses dt
straight I equals 1 half integral straight e to the power of straight t open parentheses 1 half cosec squared straight t over 2 minus cot straight t over 2 close parentheses dt
Consider comma space straight f left parenthesis straight t right parenthesis equals negative cot straight t over 2 space then space straight f apostrophe left parenthesis straight t right parenthesis equals 1 half cosec squared straight t over 2
straight I equals fraction numerator negative 1 over denominator 2 end fraction straight e to the power of straight t cot straight t over 2 plus straight c
straight I equals fraction numerator negative 1 over denominator 2 end fraction straight e to the power of 2 straight x end exponent cotx plus straight c end style
Answered by Sneha shidid | 29 Oct, 2018, 09:55: AM
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