2-0-sinx-cosx-dx-2cos-2-x-3sin-2-x-

Question Number 17033 by arnabpapu550@gmail.com last updated on 30/Jun/17

\int_{\frac{Π}{2}}^{0} \frac{sinx cosx dx}{{2 \cos}^{2} x + {3 \sin}^{2} x}

Answered by sma3l2996 last updated on 30/Jun/17

t = s i n x \Rightarrow d t = c o s x d x

I = \int_{1}^{0} \frac{t d t}{2 + t^{2}} = \frac{1}{2} {[l n ∣ 2 + t^{2} ∣]}_{1}^{0} = \frac{1}{2} (l n 2 - l n 3) = \frac{1}{2} l n \frac{2}{3}

Commented by arnabpapu550@gmail.com last updated on 30/Jun/17

Thank you very much .