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Problem

Determine whether each integral is convergent or …

02:26

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Problem 23 Medium Difficulty

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

$ \displaystyle \int_{-\infty}^0 \frac{z}{z^4 + 4}\ dz $


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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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Top Calculus 2 / BC Educators
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Missouri State University

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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

Problem 1
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Problem 4
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
Problem 23
Problem 24
Problem 25
Problem 26
Problem 27
Problem 28
Problem 29
Problem 30
Problem 31
Problem 32
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Problem 40
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Problem 47
Problem 48
Problem 49
Problem 50
Problem 51
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Problem 53
Problem 54
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Problem 59
Problem 60
Problem 61
Problem 62
Problem 63
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Problem 66
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Problem 69
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Problem 75
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Problem 77
Problem 78
Problem 79
Problem 80
Problem 81
Problem 82

Video Transcript

the problem is determined why the h Integral is convergent or divergent evaluated those that are converted. But this improper integral by definition this is equal to eliminate it. Hey, goes to negative Infinity, integral from 8 to 0 of function is the over 32 four plus two. The see we compute is definitely integral first. So for that this definitely integral First we can use use substitution that u is equal to Z square then see you D u is equal to choosy Dizzy Now we can read Write this definitely integral as integral Here this is from a square she's zero and this one half ew over you, Squire us or this is equal to one over one half times integral of a Squire zero of one over you square us two square You we know anti derivative of this function. It's act tenant you over two times one half This is the echo to one half um, one half, uh, tenant you over. So from Esquire 20 Yes, it's Echo two 1/4 acting and 00 So this is zero minus a tenant. Mhm a square over to we know when he goes to negative. Infinity A Squire over to goes to infinity. An act tenant a square over to goes to Hi, Laura two. So for this function improper, integral. This is equal to negative one force times high over to this Is the culture negative high over eight?

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Top Calculus 2 / BC Educators
Grace He

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Boston College

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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.

Join Course
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