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Use a graph to give a rough estimate of the area of the region that lies beneath the given curve. Then find the exact area.

$ y = x^{-4} $, $ 1 \le x \le 6 $

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00:47

Frank Lin

Calculus 1 / AB

Chapter 5

Integrals

Section 3

The Fundamental Theorem of Calculus

Integration

Baylor University

Idaho State University

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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Finding the Area Under a C…

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$49-52$ Use a graph to giv…

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Use a graphing calculator …

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Use a definite integral to…

Okay. This shaded region is the area we know. It's from 1 to 3, which is about 1/3 of a square unit. So now to write out are integral. Okay, Remember when we integrated increased the exponents by one divide by the new exponents and we end up with 215 divide by 648.

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