I was talking to a girl I know who's an engineering major (I was think about becoming one), and she said that she has class from 9:00 - 12:30 every day, and then spends the rest of her time, up until about midnight, doing homework. Except for Friday nights and possibly Saturdays.
Is this true...
Well now I feel a bit ridiculous. But I end up with /inte^u * u^-2. Is there a way to solve this without integration by parts? We haven't gotten to it yet so I feel like there should be a way.
Sorry for the lack of formatting, typing on my phone and I can't remember most of the tags.
\int \frac{e^{\sqrt{x}}}{\sqrt{x}}
It's in the substitution rule/symmetric function section of my book, so I figure I probably have to use one of those techniques to solve it. I've tried doing a bunch of different u substitutions \sqrt{x}, e^{{\sqrt{x}}}, etc, but none of them seem right...
Thanks to everyone who answered, although I don't know how much better it made my gut intuition feel.
I think this actually makes me feel the most relieved. With pretty much everything in Calculus it's like, "why would THAT be the case?! This makes no sense!" But I took Calc in high...
I'm about one week into a Calc II course, and I realized that I have no idea why finding the area under the curve (integrating) would be the inverse operation of finding slope (differentiating). I get that they are opposites, but not why that should be the case... it's not at all intuitive. Is...