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

$ \displaystyle \int_{-1}^2 \frac{x}{(x + 1)^2}\ dx $

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Calculus 2 / BC

Chapter 7

Techniques of Integration

Section 8

Improper Integrals

Integration Techniques

Campbell University

Oregon State 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 getting wider. Each integral is converted over skyward and wild about the tales that converted base one acts goes to next. One. Dysfunction. The denominator of dysfunction goes to zero. This's an improper, integral after mission. This is equal to Lim. A toast to make one from right hand side Andi into grow is a from a too two act's over past one squire the ex. So we computed the definite into zero first. But this definitely eating girl we can read. Write. It's a function X plus one over us. One squire, minus one over express one square The ice. Yeah. Then this's a yuko to Ellen. Ex us Juan from a too minus negative one over X paswan from a tutu, This is Echo Two, Ellen three minus. How in a cross want Andre? Here's this in class one third, minus one over a plus one. We can read like his dysfunction eyes How in three US one third, minus X plus one One here is a eh Right here a swan. How plus one A swan over a swan. Look at this function. When a goes to next to one a plus one goes to zero. It's a press want times how in a swan. But this dysfunction it goes to zero. So the whole function goes to infinity. So this interview is that word?

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