9-1-x-8-3-2-dx-

Question Number 136906 by leena12345 last updated on 27/Mar/21

\underset{9}{\int^{\infty}} \frac{1}{{(x - 8)}^{\frac{3}{2}}} d x

Answered by Dwaipayan Shikari last updated on 27/Mar/21

= - 2 {[{(x - 8)}^{- \frac{1}{2}}]}_{9}^{\infty} = - 2 (- 1) = 2

Answered by Mathspace last updated on 27/Mar/21

I = \int_{9}^{\infty} \frac{d x}{{(x - 8)}^{\frac{3}{2}}} =_{x - 8 = t} \int_{1}^{\infty} \frac{d t}{t^{\frac{3}{2}}}

= \int_{1}^{\infty} t^{- \frac{3}{2}} d t = {[\frac{1}{- \frac{3}{2} + 1} t^{- \frac{3}{2} + 1}]}_{1}^{\infty}

= {[- 2 t^{- \frac{1}{2}}]}_{1}^{\infty} = - 2 {[\frac{1}{\sqrt{t}}]}_{1}^{\infty}

= - 2 (- 1) = 2