Question

integration problem

Answer 1

\[\int\limits_{0}^{2\pi}\sqrt{(1+\sin \theta)^{2}+\cos ^{2}\theta} d \theta\]

Answer 2

*

Answer 3

sqrt[(1+sin(t))^2 + cos(t)^2] = sqrt(2) * sqrt(1+sin(t))

x = sin(t)
dx = cos(t)dt -> dt = dx/cos(t) -> dt = dx / sqrt(1-x^2)

so

integral of sqrt(2) * sqrt(1+x) * dx / sqrt(1-x^2) =
integral of sqrt(2) * dx / sqrt(1-x)

can you do it now ? be careful with the limits .. we divided by (1+x) and there is still (1-x) in the denominator