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

$ \displaystyle \int_{-2}^3 \frac{1}{x^4}\ dx $

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Calculus 2 / BC

Chapter 7

Techniques of Integration

Section 8

Improper Integrals

Integration Techniques

Harvey Mudd College

Idaho State 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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Determine whether each int…

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the problem is determine why the rich in the bureau is compartment or that wouldn't you violated those that are convergent forthis improper? Integral. A definition. We can write this integral ads into girl from next to zero one over. Access to force the axe bus. There are three one over access to force the axe. This one acts is equal to zero denominator. With this function is zero. This is a proper integral. We need to compute it. A choo Improper Auntie goes now we computed to first. What a definition this's equal to limit a goes to zero from left hand side. This is the girl from next to a of function one over x two or the here we computed to death meeting a girl first. But this is definite. Integral. This is a culture one over negative. All class one. I'm stacks too. Thank you for us, Juan. From negative to tow A. This is because to make tio one third us to make you three from negative too. No way. Yeah, this's Nico to negative One third external active. Well, uh a to make you three minus negative two to make you three. Yeah, Thanks. my a goes to zero a to make you three goes to infinity So the interviewer or the first improper integral is that weren't so for this function. So for the function one over X to force antihero from neck to two to three was this function is their word.

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