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Prove (7) using an area argument similar to the one used in the text in the case (a) $c<a$ and (b) when $c>b$.

Calculus 1 / AB

Chapter 5

Integration and its Applications

Section 6

The Definite Integral

Integrals

Oregon State University

Baylor University

University of Michigan - Ann Arbor

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.

01:02

Use an indirect proof to p…

01:24

Show that the formula Area…

suppose a policy is bigger than a require Toby policy. Then we can subtract C from both the sides to get that a place C minus e. Still, because the report a B plus C minus e no, this is a little shapeless. C minus e and this is B plus C minus. E no. C minus. E u zero plus zero is zero. So we get their day is bigger than the report. Toby. No, this is a contradiction because we know there is less than B. Therefore, it, let's see, is smaller than people say.

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