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CBSE Class 12-science Answered

Integration cos4 2x dx explain in great detail
Asked by haroonrashidgkp | 06 Oct, 2018, 11:16: PM
answered-by-expert Expert Answer
begin mathsize 18px style integral cos to the power of 4 straight x space dx equals integral cos cubed straight x. cosx space dx equals sinx space cos cubed straight x plus 3 integral sin squared straight x space cos squared straight x space dx space equals sinx space cos cubed straight x plus 3 integral open parentheses 1 minus cos squared straight x close parentheses space cos squared straight x space dx equals sinx space cos cubed straight x plus 3 integral open parentheses cos squared straight x minus cos to the power of 4 straight x close parentheses space dx integral cos to the power of 4 straight x space dx equals sinx space cos cubed straight x plus integral 3 cos squared straight x space dx minus integral 3 cos to the power of 4 straight x space dx 4 integral cos to the power of 4 straight x space dx equals sinx space cos cubed straight x plus integral 3 cos squared straight x space dx equals fraction numerator sinx space cos cubed straight x over denominator 4 end fraction plus 3 over 4 integral cos squared straight x space dx now comma integral cos squared straight x space dx equals integral sinx space cosx space dx equals cosx space sinx space plus space straight x space minus integral cos squared straight x space dx integral cos squared straight x space dx equals fraction numerator cosx space sinx over denominator 2 end fraction plus straight x over 2 Substituting space in space the space expression space above straight I space equals equals fraction numerator sinx space cos cubed straight x over denominator 4 end fraction plus 3 over 4 open parentheses fraction numerator cosx space sinx over denominator 2 end fraction plus straight x over 2 close parentheses end style
Answered by Arun | 08 Oct, 2018, 11:47: AM

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