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

$ \displaystyle \int_0^1 \frac{e^{\frac{1}{x}}}{x^3}\ dx $

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$\infty$, Divergent

Calculus 2 / BC

Chapter 7

Techniques of Integration

Section 8

Improper Integrals

Integration Techniques

Oregon State University

University of Nottingham

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, it's only wider. Each indeed growing is converted. Or that wouldn't you violated those that are convergent this improper? Integral by definition, This is Nico to limit. Hey, goes to They're all from but inside. Integral Off a to one into one Arax, over Cuba the ex. Now we compute this staff meeting to hear o first. Here we use math. My third of use institution at you is go to one over. Axe that do you is ICO to make Tio fund over X square? Yes. No. Now just staff meeting into girl because into girl from one over, eh? One eat you and the bead to you. One over X cube. The X is equal to negative. You, you So we can write. This's he got to into girl from Juan too. One of a you have into you. You here We use the my third with integration. My powers. This is Rico too integral from one who want over, eh? You! You You too. You This's the ego too. You tapped into you from Want one over, eh, Linus? Into girl. One, two, one over, eh? Into you, You! This is equal to you have each of you my ass into you from one one over, eh? And this is legal too. One over, eh? My wand into one of a minus one times into one minus one zero. Now localities, function What a goes toe hero from right inside Wonder why a goes to infinity This is infinity Infinity! Infinity times infinity! This's goes to infinity! Thiss improper Integral is divergent.

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