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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 = \sqrt[3]{x} $, $ 0 \le x \le 27 $

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00:50

Frank Lin

Calculus 1 / AB

Chapter 5

Integrals

Section 3

The Fundamental Theorem of Calculus

Integration

Missouri State University

Campbell University

Baylor 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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$49-52$ Use a graph to giv…

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Okay. We know our graph would look a little something like this. So our area would be from 0 to 27 cube root of ax D backs. I remember the expert increases by one. So increases from 1/3 to 4/3. Divide by the new exponents. Substitute 243 to about that floor.

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