Integral Applications: Rate of Change

olicoh
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Hey guys,
I was wondering if you could just check this problem for me (I put it in a Word Document and attached it to this post).

The problem, my work, and my attempted solution is included in it.

Thanks!
 

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looks correct.
 
Very nicely formatted!

A couple of suggestions:
1) Include dt in your integral, like so
\int_0^{15}\left(\frac{40}{(2t + 1)^2}-60\right)dt
2) Write your answer as a sentence, not an equation, and include units.
 
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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