# Math Help - integral help! urgent!

1. ## integral help! urgent!

integral of (x^(1/2))e^(x^(1/2))

upper limit = 4
lower limit = 0

how do I do this?

2. Originally Posted by khood
integral of (x^(1/2))e^(x^(1/2))

upper limit = 4
lower limit = 0

how do I do this?
I have found that u-substitution is the most useful method of indefinite integration

$\int\sqrt{x}e^{\sqrt{x}}~dx$

Let $\sqrt{x}=z\implies x=z^2$ so $dx=2z~dz$ so our integral becomes

$\int\sqrt{x}e^{\sqrt{x}}~dx\stackrel{\sqrt{x}=z}{\ longmapsto}2\int ze^{z}\cdot z~dz$

which can be done by parts.

3. i keep getting the wrong answer when i use that method

4. Originally Posted by khood
i keep getting the wrong answer when i use that method
Why not try posting some of your computations?

5. when i use integration by parts I end up with a^2e^2 - 2ae^a + 2e^a
(all the a's evaluated from 2 to 0) the answer im looking for is 53.598 according to the integral function on my calculator but I don't get anything close to that

6. Originally Posted by khood
when i use integration by parts I end up with a^2e^2 - 2ae^a + 2e^a
(all the a's evaluated from 2 to 0) the answer im looking for is 53.598 according to the integral function on my calculator but I don't get anything close to that
\begin{aligned}2\int_0^2 x^2\cdot e^x~dx&=2x^2\cdot e^x\bigg|_{x=0}^{x=2}-4\int_0^2 x\cdot e^x~dx\\
&=8e^2-\left(4x\cdot e^x\bigg|_{x=0}^{x=2}-4\int_0^2 e^x~dx\right)\\
&=8e^2-8e^2+4e^x\bigg|_{x=0}^{x=2}\\
&=4e^2-4\end{aligned}

Im sure you can fill in the missing steps