calculate-0-pi-sinx-1-cos-2-x-dx-

Question Number 38122 by maxmathsup by imad last updated on 22/Jun/18

c a l c u l a t e \int_{0}^{π} \frac{s i n x}{\sqrt{1 + {c o s}^{2} x}} d x

Answered by tanmay.chaudhury50@gmail.com last updated on 22/Jun/18

t = c o s x d t = - s i n x d x

\int_{1}^{- 1} \frac{- d t}{\sqrt{1 + t^{2}}}

\int_{- 1}^{1} \frac{d t}{\sqrt{1 + t^{2}}}

l

=∣ l n (t + \sqrt{1 + t^{2}}) ∣_{- 1}^{1}

= l n (1 + \sqrt{2}) - l n (- 1 + \sqrt{2})