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In the remaining exercises, it is assumed you will be using a spreadsheet.Do Exercise 10 with $n=8$.

10.75

Calculus 1 / AB

Chapter 5

Integration and its Applications

Section 4

Approximation of Areas

Integrals

Missouri State University

University of Michigan - Ann Arbor

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.

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The Try Exercises for exam…

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In the following exercises…

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Okay, We have to Minus 14 in is equal to five. You wanna know there's 12? That is negative. 12. Sorry. Satisfy this equation. Meaning doesn't make the left equal. Right to find out, we're gonna do a substitution. That's our first step. So instead of in here, we're gonna have negative 12. Everything else will stay the same. So we have two minus 1/4 of negative. 12 equal five. Let's go ahead and do the simplification. Two stays the same. We have negative. Negative. Negative. 12 over floor. So negative. Well, well before is negative. Three equal to five. If left equals. Right, then it's true. This too, minus a ***. Three is like saying two plus three, which be five. So five equals five and we can say yes. Negative. 12 is a solution to this equation.

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