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Problem

Determine whether each integral is convergent or …

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Problem 30 Hard Difficulty

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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Related Courses

Calculus 2 / BC

Calculus: Early Transcendentals

Chapter 7

Techniques of Integration

Section 8

Improper Integrals

Related Topics

Integration Techniques

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01:53

Integration Techniques - Intro

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.

Video Thumbnail

27:53

Basic Techniques

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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Watch More Solved Questions in Chapter 7

Problem 1
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Problem 5
Problem 6
Problem 7
Problem 8
Problem 9
Problem 10
Problem 11
Problem 12
Problem 13
Problem 14
Problem 15
Problem 16
Problem 17
Problem 18
Problem 19
Problem 20
Problem 21
Problem 22
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Problem 24
Problem 25
Problem 26
Problem 27
Problem 28
Problem 29
Problem 30
Problem 31
Problem 32
Problem 33
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Problem 36
Problem 37
Problem 38
Problem 39
Problem 40
Problem 41
Problem 42
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Problem 44
Problem 45
Problem 46
Problem 47
Problem 48
Problem 49
Problem 50
Problem 51
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Problem 53
Problem 54
Problem 55
Problem 56
Problem 57
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Problem 59
Problem 60
Problem 61
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Problem 66
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Problem 69
Problem 70
Problem 71
Problem 72
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Problem 74
Problem 75
Problem 76
Problem 77
Problem 78
Problem 79
Problem 80
Problem 81
Problem 82

Video Transcript

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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Lectures

Video Thumbnail

01:53

Integration Techniques - Intro

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.

Video Thumbnail

27:53

Basic Techniques

In mathematics, a technique is a method or formula for solving a problem. Techniques are often used in mathematics, physics, economics, and computer science.

Join Course
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