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Determine whether each integral is convergent or divergent. Evaluate those that are convergent.
$ \displaystyle \int_1^\infty \frac{e^{\frac{-1}{x}}}{x^2}\ dx $
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Calculus 2 / BC
Chapter 7
Techniques of Integration
Section 8
Improper Integrals
Integration Techniques
Missouri State University
Campbell University
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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the problem is determined Why that this integral is component or dem urgent. First, we can use use of institution to realise dysfunction as a function which is either to integrate. We can write you is equal to negative one over acts. And then do you and Nico to one over X Squire Jax? So this part is just to be you. Then this integral is the culture e Teo, you hands you and what tax goes to one of you goes to next to one. The axe goes to infinity. One arise goes to zero. This is zero. This is not on improper. Integral. Come. Fine is it seemed integral directly. This's equal to you, Teo. Youth power from Nick to one two zero. This's he called Tio You two zero one minus You two make you wise power. So this integral is converted. Ondas value is one minus. Ito, make it your wife's power.
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