Usage of Calculus in Chemistry

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    Calculus Chemistry
Moonflower
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Hi, I am a junior, and I am currently working on a research paper on usage of calculus in chemistry.
It is hard to find good sources, so can you guys recommend me some good sites to look at?
Thanks.
 
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Perhaps try posting this in the chemistry section (if you haven't don so already).
I know next to nothing about chemistry but I've used calculus in first and second year courses in Inorganic Chemistry. Physical Chemistry seems to have a lot of math involved.
There are also things in related fields like pharmacology, such as dose response curves, that use calculus to calculate things like area under the curve and the slope of the curve which have important (and basic) interpretations in the field.

Statistics is also a field that most, if not all, scientists must know a little about. Perhaps try looking at applied statistics in chemistry - calculus is used very often in these fields to calculate probabilities, etc.
 
Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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