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Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function.

$ \displaystyle y = \int^{x^4}_0 \cos^2 \theta \,d\theta $

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01:09

Frank Lin

Calculus 1 / AB

Chapter 5

Integrals

Section 3

The Fundamental Theorem of Calculus

Integration

Missouri State University

Harvey Mudd College

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.

00:34

Use Part 1 of the Fundamen…

0:00

01:05

Find the indicated derivat…

02:25

01:58

Evaluate the integral.…

02:10

Evaluate $\int_{0}^{1} \ma…

03:05

02:56

Use integration by substit…

03:03

Evaluate the definite inte…

Find the definite integral…

07:16

Use the Fundamental Theore…

Okay, we know we can take the derivative, which gives us why one is co sign squared Times X to the fourth times. Forks, Cube. So that's just for X cubed co sign squared X to the fourth so you can just rearrange things to put the cowfish in the front.

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