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Determine whether each integral is convergent or divergent. Evaluate those that are convergent.
$ \displaystyle \int_1^\infty \frac{\ln x}{x}\ dx $
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Calculus 2 / BC
Chapter 7
Techniques of Integration
Section 8
Improper Integrals
Integration Techniques
Campbell University
Oregon State 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.
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Determine whether each int…
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the problem is determine wider. This into grow is comm Warden tte or there wouldn't First, we can use you substitution to rewrite. Is this function for function that easier to integrate? That you is gone too? Go in then. Do you? It's ego to one Our axe. Yeah, thanks this part Just to you now this into No, he got two you you and things next goes to one You I was too serious with this here. This is serious. Max goes to infinity. Alan Necks also goes to infant. Then we can use the definition of improper into girl This the code to limit he goes to profanity integration Hero toothy you you Is this the cultures meet? He goes to infinity. Andi, this is one half you too. Two from zero to t and this is you can't name it. He goes to infinity one half It's going No, this is Bennett. So this integral has burdened
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