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Using the left cndpoint with $n=4,$ approximate the area of the region bounded by $f(x)=x^{2}+2$ and the $x$ -axis for $x$ between 0 and $2,$ see Figure 14.

5.75

Calculus 1 / AB

Chapter 5

Integration and its Applications

Section 4

Approximation of Areas

Integrals

Oregon State University

Harvey Mudd College

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.

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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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Determine the area of the …

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Hello Everybody. We're going to solve a problem number 66. Chapter number five. Integration section number two. Area. This question we have to use the point rule with an equal full to approximate. Uh The area of the region bounded by X equals X. To the bar X. During the interval given interval from zero 22. Okay. Okay. So in uh our main function as effects equal X. Epsilon X. Okay. From zero until two. Okay I'm given an equal four. Okay so let's ci equal X. Oy plus X. I -1 over to. Okay dr X will be equal to minus 0/4. It will be 1/2. Okay so C1 will be equal 1/4. C two. This will be equal 3/4. C3 will be equal 5/4. And C four will be equal 7/4. Okay so now we can substitute in the earlier formula area. Almost equal some mission or sigma from I equal one to end F. Of C. Hi delta X. Okay so it will be sigma from equal one until 4 of uh C. E. Some of our C. I multiply one over to as delta X. So we can Take 1/2. Uh As a common factor. Okay. For delta X will be 1/2. 0.321 01 Plus 1.5 eight. Southern Southern five Plus 4.36 two mine three plus 10.070 five. Why? Okay so finally in the area but almost equal um eight or 8.17. I love it. Unit squared. Thanks for watching anti litter in the next question.

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