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Use the previous exercise to determine $G^{\prime}(x)$ if $G(x)=\int_{0}^{x^{2}} \sqrt{x^{2}+1} d x$.

$$2 x \sqrt{x^{4}+1}$$

Calculus 1 / AB

Chapter 5

Integration and its Applications

Section 7

Substitution and Properties of Definite Integrals

Integrals

Missouri State University

Campbell University

Baylor University

University of Nottingham

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.

01:56

Determine $G(x)$.$$G(x…

00:43

Find $G^{\prime}(x)$.$…

05:54

Use integration by parts t…

04:50

01:41

Determine $\int \frac{1}{\…

0:00

Find

02:01

Find the Integral

04:51

Find the Integral of \int …

01:50

find the indefinite integr…

Evaluate the following.. <…

01:26

answer please

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