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If $ f $ is continuous and $ \displaystyle \int^4_0 f(x) \, dx = 10 $, find $ \displaystyle \int^2_0 f(2x) \, dx $.

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01:14

Frank Lin

Calculus 1 / AB

Chapter 5

Integrals

Section 5

The Substitution Rule

Integration

Harvey Mudd College

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.

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given the fact that we have the integral from zero to after Relax de axe, we know he can write. Are you asked you Axe conclude the two d X is do you? Which means we now have 1/2 times integral from 0 to 2, half to axe times to Jax, which means we have 1/2 of a CIA control from zero for after backs DX. Then we know this is equivalent to 10. It's given. This is my problem. We have 1/2 times 10 5 which is our solution.

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