Question

Improper integrals (equation to follow). Please help me do this problem!

Answer 1

\[\int\limits_{0}^{\pi}\frac{ 1 }{ \sqrt{x} } e^{-{\sqrt{x}}}dx\]

Answer 2

The given integrand is undefined when x = 0, so the lower limit will have to be expressed differently:
\[\lim_{a\to 0}\int_{a}^{\pi} \dfrac{1}{\sqrt{x}}e^{-\sqrt{x}} dx\]
Let
\[u = \sqrt{x}\\
du=\dfrac{1}{2\sqrt{x}} dx\\
2\sqrt{x}\;du = dx\\
2u \;du = dx\]
Make the appropriate substitution and see what happens.