Net Change Theorem: Solving for Time of Ball Dropped from 6 Story Building

sunny12
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A ball is thrown upward at 90 ft/sec from the top of a 6 story building. How long will it take before the ball lands on the sidewalk below?

This is what I have so far:

_{0}∫^{t} 90t dt

General statement for the fundamental theorem of calculus (_{a}∫^{b} f(x) dx=F(b)-F(a)).
 
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We aren't really supposed to help you if you haven't followed a form similar to what is laid out for you when you begin a post, and especially not if you haven't shown any effort in completing the problem yourself.

Why don't you tell us what you've done so far, and where you are having trouble, and we can help you from there.
 
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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