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Using the right endpoint with $n=4,$ approximate the area of the region bounded by $f(x)=4-x^{2},$ and the $x$ -axis for $x$ between -2 and $2,$ see Figure 17.

8

Calculus 1 / AB

Chapter 5

Integration and its Applications

Section 4

Approximation of Areas

Integrals

Missouri State University

Campbell University

Baylor University

Idaho State University

Lectures

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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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Use the Midpoint Rule with…

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Hello Everybody. We are going to solve the problem. # 62. Sorry uh chapter number five. Integration section number two period. Okay in this question we have to use midpoint rule with an equal four. To approximate the area of the region bounded by the graph of F. X. Equals X squared plus four X. During the governor interval from 0 to 4. Okay so our main function is to fix equal X squared plus four X. Okay. And we have an interval from 0 to 4 And an equal four. Okay. Okay so let ci equal X Plus X -1 over to. Okay. Okay so those spikes will be equal to four minus 0/4. It will be equal one. And By substituting in the Formula So C1 will be equal 1/2. C two Will be equal 3/2. C. 3 12. Equal 5/2. And finally c. 4 12 equal 7/2. Okay so now we can substitute in the area formula. Okay so earlier to the OEMs equal some mission from equal one to end F. Of C. I. Delta X. Okay so it will be Sigma from our equal one 24 of C. O. I squirted loss for C. I. Multiply the tax for one. Okay so it won't be um 1/4. Okay we can get one other common factor. Okay so we can write it. Okay so 1/4 plus two. Okay. Loss 9/4 plus six. Lost. 25/4 plus 10. Okay. Plus 49. over four plus 14. Okay and that's all multiplied one as a common factor of the text. Okay? Finally, so it will be equal 53 unit squared. Okay. Thanks for watching. Until later and the next question.

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