Hi, I'm new to integration. Can anyone help me figure out where I went wrong?
Many thanks.
Q. Evaluate the following:
Please see attachment.
You haven't taken into account the $\displaystyle x$ on the numerator.
We have:
$\displaystyle \int^4_0{\frac{x}{\sqrt{2x+1}}}dx$
I'm going to let $\displaystyle u^2=2x+1$ so that $\displaystyle 2u~du=2~dx$ and $\displaystyle dx=u~du$
When $\displaystyle x=4$, $\displaystyle u=3$ and when $\displaystyle x=0$, $\displaystyle u=1$
I have:
$\displaystyle \int^4_0{\frac{x}{\sqrt{2x+1}}}dx$
=$\displaystyle \int^3_1{\frac{u^2-1}{2u}}\cdot{u}~du$
Take it!
The parts version...
... where (key in spoiler) ...
Spoiler:
__________________________________________________ __________
Don't integrate - balloontegrate!
Balloon Calculus; standard integrals, derivatives and methods
Balloon Calculus Drawing with LaTeX and Asymptote!