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Sketch the region enclosed by the given curves and calculate its area.

$ y = x^3 $, $ y = 0 $, $ x = 1 $

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01:10

Frank Lin

Calculus 1 / AB

Chapter 5

Integrals

Section 3

The Fundamental Theorem of Calculus

Integration

Oregon 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.

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.

04:00

Sketch the region enclosed…

07:15

04:52

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10:42

Sketch the region bounded …

03:20

06:18

10:21

okay. We know we're only looking at the positive side because we know in this context, we can only have positive area. Okay, so now we over area is from 01 x cubed Jax. And I remember how we integrate increase The exploited by one's own. Just four instead of three were dividing by the new explain it, which is four now we're plugging in. This is officer just zero, Which means we have 1/4 is our solution.

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