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

$ \displaystyle \int_3^\infty \frac{1}{(x - 2)^{\frac{3}{2}}}\ dx $

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Calculus 2 / BC

Chapter 7

Techniques of Integration

Section 8

Improper Integrals

Integration Techniques

Campbell University

Baylor University

University of Michigan - Ann Arbor

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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Determine whether each int…

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Determine whether each imp…

03:56

so the problem is determined. Why does this Indigo Royals component that Wouldn't. This is an improper, integral my definition. This's Iko too. That limit off he goes to infinity into girl off dysfunction One over X minus two. Yeah. Three over to power from three tea, Jax. And then this is a coach is a limit. He goes to infinity and we need to integrate dysfunction that this is a con too negative. Two times X minus two makes you want half around the rain too. This this culture is a limit. He goes to infinity. So we need to plug in Teo three years. So this is next you two hams minus two, two, ninety one, half minus one. And we know when he goes to infinity. He minus two to ninety one. Half power zero. This is that you got to next. You two halves next you want to. This is two. So this integral is commitment. Ondas value is two

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