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Problem

The integral $$ \int_0^\infty \frac{1}{\sqrt{x} …

04:49

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Problem 54 Medium Difficulty

Use the Comparison Theorem to determine whether the integral is convergent or divergent.

$ \displaystyle \int_0^\pi \frac{\sin^2 x}{\sqrt{x}}\ 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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Oregon State University

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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 15
Problem 16
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Problem 31
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Problem 34
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
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Problem 59
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Problem 61
Problem 62
Problem 63
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Problem 65
Problem 66
Problem 67
Problem 68
Problem 69
Problem 70
Problem 71
Problem 72
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Problem 75
Problem 76
Problem 77
Problem 78
Problem 79
Problem 80
Problem 81
Problem 82

Video Transcript

the problem is, use a comparison theory, um, to determine whether the integral is converted or that burden here we will use one result this integral from you're from zero to pi. One hour acts to his power. So here you can replace pie to any number eight Any council number eight This is the verdant if he is greater than one and the calmer didn't yes is smaller than what Now our function is sine x square over route of blacks This integral from zero to pi dysfunction Sign square over root of facts Jacks Since signing a square is always smaller than one, this function is smaller than one over acts to one half smile with the ex. No, look at here. So one half is smaller than one. Mhm. This integral is convergent by comparison. Their realm the integral from zero to pi over the function syntax square root of wax is also convergent

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Related Topics

Integration Techniques

Top Calculus 2 / BC Educators
Heather Zimmers

Oregon State University

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Baylor University

Kristen Karbon

University of Michigan - Ann Arbor

Samuel Hannah

University of Nottingham

Calculus 2 / BC Courses

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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