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Suppose you are estimating the area bounded by some curve and the $x$ -axis, between the lines $x=0$ and $x=2 .$ If you are using $n=4$ rectangles, determine the $x$ -values that form the partition of the interval, that is, the $x$ -values needed in determining the heights of the rectangles.

$\{0,0.5,1,1.5,2\}$

Calculus 1 / AB

Chapter 5

Integration and its Applications

Section 4

Approximation of Areas

Integrals

Campbell University

Baylor University

University of Michigan - Ann Arbor

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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So here Delta X is going to equal four minus negative for Over four. Which is equal to two man four is going to equal f times negative. Two times delta x plus stuff. Zero times DELTA X plus staff of two times delta X. Applause Theft of four. I'm still tax what? Which is equal to -2? I was two plus zero. Yeah Plus two trials to Yeah it was for hold on. I didn't take an account actual functions like that. It's just negative too. Times two Okay. Was to I was 10 maybe two plus something wanted to 1st 10 times two. zero. Sorry, 0 plus 10 times too plus. Okay. Yeah, two Times two Plus 10. That's too Plus four times 2 plus 10 times two. Which is equal to 28 plus 20 plus 28 plus 52 which is equal to one. units scored.

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