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

$ \displaystyle \int_1^\infty \frac{1}{x^2 + x}\ dx $

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convergent to $\ln 2$

Calculus 2 / BC

Chapter 7

Techniques of Integration

Section 8

Improper Integrals

Integration Techniques

University of Nottingham

Idaho State University

Boston College

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 whether this integral is cordant or divergent the first by definition, of an improper integral. This is equal to the limit. He goes to infinity. That's integral from one to t bond over X square US X, the axe Mhm. And this is echo to limit. He goes to infinity Integral 12 t We can rewrite this function as one over acts times X plus one. Yeah. Now this is the echo to the limit He goes to infinity Integral one, the T Also, we can rewrite this function as one over X minus one over X as one the X Now we can write this. This is equal to the limit. He goes to infinity as anti derivative of one Iraq's Ln acts This anti derivative of one over X plus one is Ln X plus one from one to keep. This is echo is the limit He goes to infinity Ln X over X plus one and wanted to. This is a co two limit. He goes to infinity Alan she over walk one last T minus now and 1/2. When he goes to infinity, she over one plus t goes to one, so l m t over one plus t goes to zero. The answer is equal to negative Ln one half. And this is also the co two Ln two mhm. So this integral is concordant and this value is l N two.

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