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

$ \displaystyle \int_0^5 \frac{w}{w - 2}\ dw $

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Calculus 2 / BC

Chapter 7

Techniques of Integration

Section 8

Improper Integrals

Integration Techniques

Campbell University

Harvey Mudd College

University of Nottingham

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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$5-40$ Determine whether e…

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The problem is determine whether each integral is converted or diverted and violated those that are converted for this improper, integral definition. This is equal to 0 from 0 to 2, w over w minus 2 d, w integral from 2 to 5, w over w minus 2 d. W we computed the first integral this integral by definition, this is equal to the limit a goes to to integral, from 0 to a w over w minus 2 d, w located as definite integrale integral equals. This is 0 to a. We can rewrite this his function as w minus 2 over w minus 2 plus 2 over w minus 2. This is equal to first thing is 1 to this plus 2 times n absolute value of w minus 2 point from 80 to a this is equal to a plus 2 times: l n 2 minus a minus 2 times. L n to s on a goes to 2, is it from left hand, side and a goes to 2 from right hand, side on 2 minus a goes to negative infinity. So this answer goes to negative infinity point. Hence intent.

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