Question

Evaluate integral dx/(1+sinx) from limits pi/4 to pi/2

Answer 1

Integral=dx/(1+sinx) from limits pi/4 to pi/2

Take the integral

Integral 1/sin x+1 dx

For the integrand, substitute

u=tan(x/2)

sin x=2u/(u^2+1)

cos x=(1-u^2)/(u^2+1)

dx=2du/(u^2+1)

=integral 2/(u^2+1)(2u/(u^2+1) +1)

=2 sin(x/2)/(sin (x/2)+cos(x/2)) +c