Parts will get you there. How did you do it?
You may wish to simplify your life a little, unless you are married to significant figures, and rewrite as .
Hi all, I need some help. I'm taking system dynamics and control over the summer, but it's been over 3 years since my last calculus course, and some of these integrals are killing me.
is evaluated to be
before plugging integration limits, but I can't even get here.
I've tried substituting the lower half with X, then going from there which gets me a partial answer, and I've tried integrating by parts. I'm so out of mental shape it hurts.
where does the leftover H term go? do you just consider it another constant now? and how do I have to alter the limits of integration for this again?
I would really appreciate it if you could just give me a step by step. This would be like a quick review, then. I took calc 1 in 2004, I haven't been in school for 2.5 years, and I'm jumping back to finish my last year playing catchup in higher engineering classes, and I learn best by seeing a solution then picking it apart.
I don't think parts is working for you there - getting your u's and du's muddled. I would of course recommend lazy integration by parts...
... but not in this case. A simple u-sub would be H = u^2.
Just in case a picture helps...
i.e. replace H with something... as we said, u^2...
... where (key in spoiler) ...
Don't integrate - balloontegrate!
Balloon Calculus; standard integrals, derivatives and methods
Balloon Calculus Drawing with LaTeX and Asymptote!