Integration dx/( a cos x + b sin x)2 a> 0 and b>0  explain in great detail

Asked by haroonrashidgkp | 6th Oct, 2018, 11:17: PM

Expert Answer:

begin mathsize 16px style straight I equals integral open parentheses acosx plus bsinx close parentheses squared dx
straight I equals integral open parentheses straight a squared cos squared straight x plus 2 absinxcosx plus straight b squared sin squared straight x close parentheses dx
straight I equals integral open parentheses straight a squared cross times fraction numerator 1 minus cos 2 straight x over denominator 2 end fraction plus absin 2 straight x plus straight b squared cross times fraction numerator 1 minus cos 2 straight x over denominator 2 end fraction close parentheses dx
straight I equals straight a squared over 2 open parentheses straight x minus fraction numerator sin 2 straight x over denominator 2 end fraction close parentheses minus fraction numerator abcos 2 straight x over denominator 2 end fraction plus straight b squared over 2 open parentheses straight x minus fraction numerator sin 2 straight x over denominator 2 end fraction close parentheses plus straight c end style

Answered by Sneha shidid | 11th Oct, 2018, 10:50: AM