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Evaluate the integral.

$ \displaystyle \int^2_1 \frac{v^3 + 3v^6}{v^4} \,dv $

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$$\ln 2+7$$

00:45

Frank Lin

Calculus 1 / AB

Chapter 5

Integrals

Section 3

The Fundamental Theorem of Calculus

Integration

Campbell University

Oregon State University

Harvey Mudd 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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integrate, which means increase our exponents by one and divide by the new exponents. So we know the integral of one over V is simply gonna be natural. Log V right? This is a property. So now we can plug in. Natural of one is simply zero giving us not to work with two plus seven.

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