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

$ \displaystyle \int_1^\infty \frac{1 + \sin^2 x}{\sqrt{x}}\ dx $

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Calculus 2 / BC

Chapter 7

Techniques of Integration

Section 8

Improper Integrals

Integration Techniques

University of Michigan - Ann Arbor

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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.

01:45

Use the Comparison Theorem…

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problem is used that he comparison theory, um, to determine why this integral discordant or there wouldn't. First, we have the following result and to grow from one to infinity off of the function one over ice to peace Power Jax on What's this integral? This integral is convergent If he is greedy is online on the divergent If is smaller than one now So our integral off this function Now just listen to girl from one to infinity one plus sign I squire over motive ax the ax This scientific square is created and zero so dysfunction always bigger is one over you tell blacks this's really on the fourth dysfunction. The cat is a result here this is ax to one half He is They go to one half, Then we're half is small One is this function that word didn't Now our function is greeted and dysfunction. Our function is how so That wouldn't buy the cereal off comparison cereal

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