`int_1^18(sqrt(3/z))dz` Evaluate the integral.

Evaluate $\displaystyle{\int_{{1}}^{{18}}}{{\left(\frac{{3}}{{z}}\right)}}^{{\frac{{1}}{{2}}}}{\left.{d}{z}\right.}$

$\displaystyle={\int_{{1}}^{{18}}}\sqrt{{{3}}}{{z}}^{{-\frac{{1}}{{2}}}}{\left.{d}{z}\right.}$

$\displaystyle=\sqrt{{{3}}}{\int_{{1}}^{{18}}}{{z}}^{{-\frac{{1}}{{2}}}}{\left.{d}{z}\right.}$

Integrate the function.

$\displaystyle=\sqrt{{{3}}}{\left[\frac{{{z}}^{{\frac{{1}}{{2}}}}}{{\frac{{1}}{{2}}}}\right]}=\sqrt{{{3}}}{\left[{2}{{z}}^{{\frac{{1}}{{2}}}}\right]}$

Evaluate the function
from 1 to 18.

$\displaystyle=\sqrt{{{3}}}{\left[{2}{{\left({18}\right)}}^{{\frac{{1}}{{2}}}}-{2}{{\left({1}\right)}}^{{\frac{{1}}{{2}}}}\right]}$

=11.233

Spooky Notes

Wednesday, July 22, 2015

$\displaystyle{\int_{{1}}^{{18}}}{\left(\sqrt{{\frac{{3}}{{z}}}}\right)}{\left.{d}{z}\right.}$ Evaluate the integral.

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