Integral : substitution & by parts of an exponential

Hello,

Quote:

Originally Posted by **Firstone**

Hi there, I was wondering if you could steer me ikn the right direction with an assignment question. It's a definite integral question.

Integral e^(sqrt{x}) dx (from 1 to 4)

It says i'm suppose to use substiution then integration by parts.

but I can't really see why I use substitution, it didn't makew anything easier.

I let u = sqrt{x}

I ended up with Integral e^(sqrt{x}) * 2du/sqrt{x}

I was just wondering if i did the substitution part right?

No, but you didn't substitute at all (Surprised)

$\displaystyle \sqrt{x}=u \implies du=\frac{dx}{2 \sqrt{x}} \implies dx=2 \sqrt{x} ~du \neq \frac{2 du}{\sqrt{x}}$

Transform your integral : every x has to disappear. So as soon as you encounter $\displaystyle \sqrt{x}$, change it into u. If there was $\displaystyle x$ that you encounter, then $\displaystyle x=u^2$ and substitute too.

And then integrate by parts as recommended. Don't forget to either change the boundaries of the integral, either to substitute back u.

P.S. : please next time, post a new thread. It may be useful for some other people (Wink) (and my PM box is overwhelmed by all these messages lol!)