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Let $ \displaystyle F(x) = \int^x_1 f(t) \, dt $, where $ f $ is the function whose graph is shown. Where is $ F $ concave downward?

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02:00

Frank Lin

Calculus 1 / AB

Chapter 5

Integrals

Section 3

The Fundamental Theorem of Calculus

Integration

Harvey Mudd College

Baylor University

University of Michigan - Ann Arbor

Boston College

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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Let $F(x)=\int_{1}^{x} f(t…

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Let F(x)f(t) dt , wher…

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Determine where the graph …

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'Let _ F(a) be the ar…

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Find intervals where the g…

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okay for this question Over here, we know we're trying to figure out where is F Conkey downward? In order to do that, we know we're gonna have to calculate the first and the second derivative. Okay, so given this we know after box is intro from wonder Acts of off of T Do you achieve? Remember, we have the fear of the f Prime of axe is lower case of the vax therefore off Double problem Max is lower case off Problem X Therefore, we know the given graph is decreasing on the interval. Negative 1 to 1. Therefore we know it is Kong Cave down on the interval. Negative 1 to 1.

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