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Verify that $ f(x) = \sin \sqrt[3]{x} $ is an odd…
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Problem 73 Hard Difficulty

Evaluate the definite integral.

$ \displaystyle \int^1_0 \frac{dx}{(1 + \sqrt{x})^4} $

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03:01

Frank Lin

Related Courses

Calculus 1 / AB
Calculus: Early Transcendentals

Chapter 5

Integrals

Section 5

The Substitution Rule

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Integrals

Integration

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Top Calculus 1 / AB Educators
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Missouri State University

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Lectures

Video Thumbnail

05:53
Integrals - Intro

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.
Video Thumbnail

40:35
Area Under Curves - Overview

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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Video Transcript

we know that are you is one plus squirt of acts, which means that our two times you must one do you is equivalent to DX, which means the letters of integration are changed from 0 to 1 to one postcard of zero, which is one of the bottom toe one plus court of one, which is two on the top. Okay, now we're gonna be using the power rule to integrate, which means we increase the exponents by one. And then we divide by the new exponents using the fundamental damn of calculus. We can now pull again. We end up with 1/6 is our solution.

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Related Topics

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Top Calculus 1 / AB Educators
Catherine Ross

Missouri State University

Heather Zimmers

Oregon State University

Samuel Hannah

University of Nottingham

Michael Jacobsen

Idaho State University

Calculus 1 / AB Courses

Lectures

Video Thumbnail

05:53
Integrals - Intro

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.
Video Thumbnail

40:35
Area Under Curves - Overview

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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