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Find the derivative of the function.
$ F(x) = \displaystyle \int^{2x}_{\sqrt{x}} \arctan t \, dt $
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01:24
Frank Lin
Calculus 1 / AB
Chapter 5
Integrals
Section 3
The Fundamental Theorem of Calculus
Integration
Missouri State University
Oregon State University
Baylor University
Lectures
05:53
In mathematics, an indefinite integral is an integral whose integrand is not known in terms of elementary functions. An indefinite integral is usually encountered when integrating functions that are not elementary functions themselves.
40:35
In mathematics, integration is one of the two main operations of calculus, with its inverse operation, differentiation, being the other. Given a function of a real variable (often called "the integrand"), an antiderivative is a function whose derivative is the given function. The area under a real-valued function of a real variable is the integral of the function, provided it is defined on a closed interval around a given point. It is a basic result of calculus that an antiderivative always exists, and is equal to the original function evaluated at the upper limit of integration.
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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.
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