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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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Calculus 2 / BC

Chapter 7

Techniques of Integration

Section 8

Improper Integrals

Integration Techniques

Oregon State University

Baylor University

University of Michigan - Ann Arbor

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.

03:44

Use the Comparison Theorem…

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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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