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Evaluate the integral.

$ \displaystyle \int_1^5 \frac{M}{e^M} dM $

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Calculus 2 / BC

Chapter 7

Techniques of Integration

Section 1

Integration by Parts

Integration Techniques

Missouri State University

Campbell University

Baylor University

Idaho State University

Lectures

01:53

In mathematics, integration is one of the two main operations in calculus, with its inverse, differentiation, being the other. Given a function of a real variable, an antiderivative, integral, or integrand is the function's derivative, with respect to the variable of interest. The integrals of a function are the components of its antiderivative. The definite integral of a function from a to b is the area of the region in the xy-plane that lies between the graph of the function and the x-axis, above the x-axis, or below the x-axis. The indefinite integral of a function is an antiderivative of the function, and can be used to find the original function when given the derivative. The definite integral of a function is a single-valued function on a given interval. It can be computed by evaluating the definite integral of a function at every x in the domain of the function, then adding the results together.

27:53

In mathematics, a technique is a method or formula for solving a problem. Techniques are often used in mathematics, physics, economics, and computer science.

02:47

Evaluate the integral.…

01:29

Evaluate.$$\int_{0}^{b…

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00:26

the problem is the valley with his integral integral from one to file and our each of the am PM For this problem, we can use my food only integration by pars. The formula is and to grow from you from what I am to be you tensely prom. Your packs. Yes. He called to you tamp swing from a to B minus into grew from a to B you from tensely yaks. Now, for our problem, we cannot you use Chico to um and B is two e to the negative And this is what we promise They goto eat connective. Then you prom if they could one on and really it's you go too negative. He too negative. Now, By using this formula, we have this into grow. It's a cultural, You know Tom's Elise, this is negative. Um, I have to Negative from one to file. Minus and two girl from one to five, your prime comes We This is class into negative e. With the first term, we can plug in five. I want to um So this is a cultural negative Five. Have you two negative five class. You two make too. Juan on the full sock in the term this integral is he goto negative. You too. Negative. From one to five. This is a connective into negative five. Plus you two make to want. So the answer is negative. Six. You too make you foul minus. This is a class two times in to make one. This's the other.

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