Evaluate the following integral I=∫_0^(π⁄2)(〖sin〗^n x)/(〖sin〗^n x+〖cos〗^n x) dx
All Answers
total answers (1)
total answers (1)
Mathematics
I=∫_0^(π⁄2)(〖sin〗^n x)/(〖sin〗^n x+〖cos〗^n x) dx →(1)
need an explanation for this answer? contact us directly to get an explanation for this answerSolution:
Since I=∫_0^(π⁄2)(〖sin〗^n (π/2-x))/(〖sin〗^n (π/2-x)+〖cos〗^n (π/2-x) ) dx
=∫_0^(π⁄2)(〖cos〗^n x)/(〖cos〗^n x+〖sin〗^n x) dx →(2)
Adding (1) and (2) we get:
2I=∫_0^(π⁄2)(〖cos〗^n x+〖sin〗^n x)/(〖cos〗^n x+〖sin〗^n x) dx=∫_0^(π⁄2)dx=π⁄2
∴I=π/4