Please give me the complete solution of 

Asked by Balbir | 23rd Oct, 2017, 08:57: PM

Expert Answer:

begin mathsize 16px style integral open parentheses asin to the power of 4 straight x plus bcos to the power of 4 straight x close parentheses dx
Using space the space formulae space for space sin squared straight x space equals space fraction numerator 1 space minus space cos 2 straight x over denominator 2 end fraction space and space space cos squared straight x space equals space fraction numerator 1 space plus space cos 2 straight x over denominator 2 end fraction
sin to the power of 4 straight x space equals space open parentheses sin squared straight x close parentheses squared
sin to the power of 4 straight x space equals space open parentheses fraction numerator 1 space minus space cos 2 straight x over denominator 2 end fraction close parentheses squared
sin to the power of 4 straight x space equals fraction numerator 1 minus 2 cos 2 straight x plus cos squared 2 straight x over denominator 4 end fraction
sin to the power of 4 straight x space equals fraction numerator 1 minus 2 cos 2 straight x plus begin display style fraction numerator 1 plus cos 4 straight x over denominator 2 end fraction end style over denominator 4 end fraction
sin to the power of 4 straight x space equals fraction numerator 2 minus 4 cos 2 straight x plus 1 plus cos 4 straight x over denominator 8 end fraction
sin to the power of 4 straight x space equals fraction numerator 3 minus 4 cos 2 straight x plus cos 4 straight x over denominator 8 end fraction
Similarly space you space can space solve space it space for space cos to the power of 4 straight x space and space integrate space further. end style

Answered by Sneha shidid | 14th Dec, 2017, 04:54: PM