integral fraction numerator sin x times cos x over denominator square root of 1 plus sin squared end root x end fraction d x

Asked by Prajapatiraj770 | 9th Jun, 2021, 09:25: AM

Expert Answer:

begin mathsize 14px style I space equals space integral fraction numerator sin x space cos x space d x over denominator square root of 1 plus sin squared x end root end fraction end style
 
Let us use the substitution ( 1 + sin2x ) = u
 
Then integration becomes 
 
begin mathsize 14px style I space equals space 1 half integral space fraction numerator d u over denominator square root of u end fraction space equals space 1 half square root of u space plus space C end style
begin mathsize 14px style I space equals space 1 half square root of 1 plus sin squared x end root space plus space C end style

Answered by Thiyagarajan K | 20th Sep, 2021, 08:57: AM