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Numerade Educator

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Problem 62 Hard Difficulty

Find the derivative of the function.

$ F(x) = \displaystyle \int^{2x}_{\sqrt{x}} \arctan t \, dt $

Answer

$$
-\frac{1}{2 \sqrt{x}} \arctan (\sqrt{x})+2 \arctan (2 x)
$$

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Video Transcript

Okay. You know, the first thing we can do is we can split this up. So we're splitting up the integral. Okay? Using the fundamental damn of calculus. We know G of X Prime is lower case G of X, which is equivalent to our pretend of acts. We have our 10 of X here, which means that we end up with negative one over to squirt of acts. Time's worth, 10 of squirt of max, plus two terms are tan of two acts cause we're just plugging in like that.