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Approximate the indicated area by connecting succesive $y^{-}$ values on the curve by a straight line, resulting in trapezoids.Use $n=4$ trapezoids to estimate the area of the region in Exercise 12.

2

Calculus 1 / AB

Chapter 5

Integration and its Applications

Section 4

Approximation of Areas

Integrals

Missouri State University

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University of Nottingham

Boston 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.

01:44

Use the Midpoint Rule with…

02:31

Approximate the area of th…

01:38

04:41

Sketch the region bounded …

01:24

and use the big point roll on this function there. This interval longtime many right angles to find out what tell taxes just going to be for four minutes. 0/4 she calls one. That means normally it would be from 0 to 1 to 2 to 3 to four. Since raising midpoint role we want one half, three house, five house and seven half. So then from here Do one times half of one half Plus f of three amps Plus half of five house I say from seven house. So that's going to be equal to 11. Plug that into the original air. Let's go ahead and find out what the actual integral this is. So from 0 to 4 for why I asked why squared That's going to be able to forli squared over two. That's why I cubed over three. Taking that from 0 to 4. So that's going to be equivalent to 64/2, 64/3. That's equal to 32 or three just equivalent to 10.6 heating. And we can compare the two And we don't definitely know that 10.6 Painting is less than 11. That's the comparison there.

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