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Differentiating an Integral Function Using Chain Rule

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Explanations 1

(Video) Fundamental Theorem of Calculus - Part 1 by PatrickJMT Here's a video by patrickJMT where he explains the Fundamental Theorem of Calculus Part 1 and how you can solve pr…
By Alex Federspiel, Gabi Slizewska

Problems 3

Let f(x)=∫x5x3et2dtf(x) = \int_{x^5}^{x^3} e^{t^2} dtf(x)=∫x5x3et2dt for all reals xxx. What is the value of f′(0)f'(0)f′(0)?
Let aaa be the positive real number minimizing the function g(a)=∫aa2dxx+xg(a) = \int_a^{a^2} \frac{dx}{x+\sqrt{x}}g(a)=∫aa2x+xdx. Find the value of a+1/aa + 1/aa+1/a. Source…
If her manager asks her to select a single, continuous 444-hour shift between 111111 AM and 111111 PM, what shift should she select to maximize the amount of tables that are occ…