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

$ \displaystyle h(x) = \int^{e^x}_1 \ln t \,dt $

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$x e^{x}$

01:54

Frank Lin

Calculus 1 / AB

Chapter 5

Integrals

Section 3

The Fundamental Theorem of Calculus

Integration

Missouri State University

University of Michigan - Ann Arbor

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.

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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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first thing we can do is look at the derivative and we need to use the chain roll for this natural of each of the AKs times you did the axe, which is the general, which gives us acts natural log of e terms. Each of the AKs extends natural water e It's simply x times one which gives us acts, eat the axe.

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