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Determine whether each integral is convergent or divergent. Evaluate those that are convergent.

$ \displaystyle \int_0^1 r \ln r\ dr $

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Calculus 2 / BC

Chapter 7

Techniques of Integration

Section 8

Improper Integrals

Integration Techniques

Oregon State University

University of Nottingham

Boston College

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.

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Determine whether each int…

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Determine whether the inte…

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the problem is determine whether each integral is coordinated. Word of urgent. You violated those that word. It thiss improper, integral that nation. This is equal to the limit. A ghost, tio zero from right hand side into go from a one r Ellen are the look at it. Is this definite? Integral to Stephanie being the girl Eco's indeed girl from a one, you know. And, uh yeah. One, huh? Ask for here. We use, um my third of integration. My parts staffing the integral is he called Tio. You are one our square. Some es juan minus into girl remained one one half square. One over r yeah, is because two flying one on a to this function. This is zero minus, eh? What a squire, my ass. This's while half off times are so on a derivative. Off this function is one force, uh, square from a one. This recall to make our end, eh, Holmes? One Hey, square minus one. Force minus one. Force a square. Hear what a goes to zero. A square goes to zero this far because two zero on ourselves This part ln aid hams. A square also goes to zero for this card, you can use NOPD toe computed. You go to a close to zero, you know, And eh Over one terms, one over a square. Then we use a low paid US rule. This is Nico to limit one over, eh? Over. This's a native one over to kill. It goes to zero. This is equal to zero. No. So the result is zero minus one Force. This is making you force. This improper into girl is confident on the value is ninety one over four.

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