find-the-value-of-dt-t-2-2t-2-3-2-

Question Number 40157 by maxmathsup by imad last updated on 16/Jul/18

f i n d t h e v a l u e o f \int_{- \infty}^{+ \infty} \frac{d t}{{(t^{2} - 2 t + 2)}^{\frac{3}{2}}}

Commented by maxmathsup by imad last updated on 16/Jul/18

l e t I = \int_{- \infty}^{+ \infty} \frac{d t}{{(t^{2} - 2 t + 2)}^{\frac{3}{2}}}

I = \int_{- \infty}^{+ \infty} \frac{d t}{{{(t - 1)}^{2} + 1}^{\frac{3}{2}}} c h a n g e m e n t t - 1 = t a n x g i v e

I = \int_{- \frac{π}{2}}^{\frac{π}{2}} \frac{(1 + {t a n}^{2} x) d x}{{(1 + {t a n}^{2} x)}^{\frac{3}{2}}} = \int_{- \frac{π}{2}}^{\frac{π}{2}} \frac{d x}{{(1 + {t a n}^{2} x)}^{\frac{1}{2}}} d x

= \int_{- \frac{π}{2}}^{\frac{π}{2}} c o s x d x = {[s i n x]}_{- \frac{π}{2}}^{\frac{π}{2}} = 2

I = 2

Answered by tanmay.chaudhury50@gmail.com last updated on 16/Jul/18

\int_{- \infty}^{+ \infty} \frac{d t}{{{(t - 1)}^{2} + 1}^{\frac{3}{2}}} l e t (t - 1) = t a n k

\int_{- \frac{Π}{2}}^{\frac{Π}{2}} \frac{{s e c}^{2} k d k}{{s e c}^{3} k}

\int_{- \frac{Π}{2}}^{\frac{Π}{2}} c o s k d k

∣ s i n k ∣_{- \frac{Π}{2}}^{\frac{Π}{2}} = 2