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Problem

Determine whether each integral is convergent or …

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Problem 18 Medium Difficulty

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

$ \displaystyle \int_2^\infty \frac{dv}{v^2 + 2v - 3} $


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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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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.

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Watch More Solved Questions in Chapter 7

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Problem 6
Problem 7
Problem 8
Problem 9
Problem 10
Problem 11
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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
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Problem 30
Problem 31
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Problem 35
Problem 36
Problem 37
Problem 38
Problem 39
Problem 40
Problem 41
Problem 42
Problem 43
Problem 44
Problem 45
Problem 46
Problem 47
Problem 48
Problem 49
Problem 50
Problem 51
Problem 52
Problem 53
Problem 54
Problem 55
Problem 56
Problem 57
Problem 58
Problem 59
Problem 60
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Problem 63
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Problem 66
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Problem 68
Problem 69
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Problem 74
Problem 75
Problem 76
Problem 77
Problem 78
Problem 79
Problem 80
Problem 81
Problem 82

Video Transcript

a definition this's ICO to limit It goes to infinity of the into girl to a function very over Wait square past two way minus three Yeah Here we first the computer to death me Tio into your off first phone just anti girl This's Iko too integral off two way We can realize dysfunction as bad over we minus one Hi Way three Dearie and dysfunction, this is you Come too one over three minus one, minus one Over with Plus really Time's over. Or do you? Then we can find on type derivative of dysfunction. This's Iko too. We might just one month while and we plus three times one over from to a This is equal to one over four No, a minus one over, eh? Class three Venice two minus one over two plus three When they goes to infinity a minus one over a plus three goes to one. So I went a max one over a plus three goes to zero disfunction goes to one over four Pam's make tive Ellen one hour five on dh. This's also Iko too. One over four Shit tamps Ellen file this improper Integral is convergent Ondas a while you is one over four camps hell in five

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Top Calculus 2 / BC Educators
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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

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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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