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

$ \displaystyle \int_0^1 \frac{1}{x}\ dx $

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Calculus 2 / BC

Chapter 7

Techniques of Integration

Section 8

Improper Integrals

Integration Techniques

Baylor University

University of Michigan - Ann Arbor

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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So the problem is determined. Why either just stingy grow as components are evident. Notice that Monex goes to zero. One of Iraq's goes to infinity. This is an improper into girl. By definition, this is a call to the limit. He goes to zero from right hand side. Integral won over acts from team one. It is the limit. He goes to infinity. Chico's to zero from right outside. Alan Ex after one little box Ground Team one. This is the cultures. And I meant it. He goes to zero from right outside. Alan one minus Ellen Kaede. Andi thinks Ellen one zero statistics Nico to the limit. He goes to zero from right hand side. Negative. Yeah. And he we know when he goes to zero from red hands that Auntie those two make to infinity. So the result is you got to infinity This integral ist evident

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