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Show that Exercise 31 may be written in the form $\frac{d y}{d x}=f\left(\frac{y}{x}\right)$

Calculus 1 / AB

Chapter 5

Integration and its Applications

Section 2

Applications of Antidifferentiation

Integrals

Oregon State University

Harvey Mudd College

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.

00:31

In Exercises $31-42,$ find…

02:37

Show that the subtangent t…

01:14

Refer to Exercise $31 .$ F…

02:13

In Exercises $33-36,$ find…

00:44

00:56

We're just taking a driven it. You could do that using the powerful. So do I get after All, right. Like that equals bring the power down. Negative. Three older five becomes the coefficient X, and then we subtract one from the exploding, as we usually do. So negative, Frits. Frits, minus one. We can write as negative. 3/5. Minus one minus 545 And that gives us the power. Negative eight when you're five and that is our derivative.

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