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Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function.

$ \displaystyle g(x) = \int^x_1 \ln (1 + t^2) \,dt $

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00:35

Frank Lin

00:22

Amrita Bhasin

Calculus 1 / AB

Chapter 5

Integrals

Section 3

The Fundamental Theorem of Calculus

Integration

Missouri State University

Campbell University

University of Nottingham

Idaho State 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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Use Part 1 of the Fundamen…

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Use the Second Fundamental…

All right, so let's move on to the next question. We're still using the same concept to fundamental form of calculus. We have a different integral, so it is going to be the G of X. A function of X is equal to the integration from 12 x natural. Log off one plus T squared DT. So I want you to listen to me carefully, OK, What this means this expression means is that it is the anti derivative of the natural log of one plus something squared, and then it's going to end up being a function off X. That's how I want you to interpret this expression right there. So again, it's an anti derivative off right here. That's a function of X. So if I take the derivative with respect to X, the anti the derivative off, the anti derivative are going to undo each other, so you will just get what's inside and remember, it's a function of X. So instead of a T square, you will see an X squared, and this is how you do this problem

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