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

$ \displaystyle \int_0^\infty \frac{x}{x^3 + 1}\ dx $

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03:04

Wen Zheng

Calculus 2 / BC

Chapter 7

Techniques of Integration

Section 8

Improper Integrals

Integration Techniques

Missouri State University

Campbell University

Boston College

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.

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Use the Comparison Theorem…

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Hello. Welcome to this lesson. In this lesson, we'll find a convergence good or divergence of the integration the comparison test. So let this be a function for backside is extra extra extra part three plus one. Let's have another function. Your ex That is X uber's the battery eggs. Oh, you have export to X over X two plus X last one. So for every value of X J of X is greater than f of X. Okay, but given the same same bounds, uh, converges in around almost one. Okay, Converges to 0.969 Okay, so F g of X is greater than f of x and Jim and Jane of X converges than f of X. Given the bounce in the integral. So it means that yeah. Of f of X Bull. Yeah, converges using the comparison tests. Sometimes your time is the end of the lesson.

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