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Solve Example 5 by first interchanging $x$ and $y$ as suggested in the note following the solution.

Calculus 1 / AB

Chapter 5

Integration and its Applications

Section 8

Applications of the Definite Integral

Integrals

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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.

00:19

Solve using any method.

00:50

Solve by substitution.…

01:06

Solve the equation for $x$…

00:39

Solve each equation for $y…

00:44

Solve for the indicated va…

03:18

Solve each system by the s…

Given the system, Y equals five X and Y equals negative 10. We can use substitution because we already know why it's negative 10. So substitute that for Y in the first one, negative 10 equals five X, divide both sides by five, and X is negative two, so the solution is negative to negative 10. Yes.

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