# calc help

• January 10th 2009, 08:25 AM
twilightstr
calc help
Make a substitution to express the integrand as a rational function and then evaluate the integral.
integral from 16 to 9 of (square root x)/ (x-4) dx (Let u= square root of x.)
Thanks
• January 10th 2009, 08:44 AM
Jester
Quote:

Originally Posted by twilightstr
Make a substitution to express the integrand as a rational function and then evaluate the integral.
integral from 16 to 9 of (square root x)/ (x-4) dx (Let u= square root of x.)
Thanks

$\int_9^{16} \frac{\sqrt{x}}{x-4}\,dx$
If $u = \sqrt{x}$ then $du = \frac{dx}{2\sqrt{x}}$ or $2 u du = dx$

So (remember - change your limits of integration)

$\int_9^{16} \frac{\sqrt{x}}{x-4}\,dx = \int_3^4 \frac{2u^2}{u^2-4}\, du$. Can you take it from here?