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Problem

Determine whether each integral is convergent or …

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Problem 34 Medium Difficulty

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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Related Courses

Calculus 2 / BC

Calculus: Early Transcendentals

Chapter 7

Techniques of Integration

Section 8

Improper Integrals

Related Topics

Integration Techniques

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01:53

Integration Techniques - Intro

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.

Video Thumbnail

27:53

Basic Techniques

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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Watch More Solved Questions in Chapter 7

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Problem 81
Problem 82

Video Transcript

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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Top Calculus 2 / BC Educators
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Lectures

Video Thumbnail

01:53

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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.

Video Thumbnail

27:53

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