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

$ \displaystyle \int_0^4 \frac{dx}{x^2 - x - 2} $

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$-\infty,$ Divergent

Calculus 2 / BC

Chapter 7

Techniques of Integration

Section 8

Improper Integrals

Integration Techniques

Missouri State University

Oregon State University

Harvey Mudd College

Idaho State University

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 the inte…

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Determine whether each imp…

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the problem is determine whether each Negro it's ca mordant world that wouldn't you know it. They thought that a word it we could write it this integral as Jiro from there to four. Yeah, over X minus two. Last one. Things one acts goes to two. Denominated goes to zero. This is proper integral a definition. This is the Goto the girl found zero to two the axe over X minus two on DH X plus one us integral from two to four. Yes, over X minus two hands one No, we computed this integral forest. But this improper into girl by definition, this's recall to limit a goes to two from left side and integral from zero to a we can't write dysfunction. That's one third times one over X minus two, minus one over X Swan. Yes. Now look at this. Definitely to grow this deafening hero Eco's one third. Oh, and after a while, you x minus two, my ass. Yeah, And express long from zero to a and this is equal to one third you on X minus two over. Ex us long? Absolutely. You from zero to a No, Andi, Since these pico to one third ln a minus two over a plus one through the wind minus on Plotting zero. Here is this the trail and two What a goes to true from last night Side a minus two Over a plus Juan goes to infinity. I saw it goes to zero. So, Ellen, a man is to over a plus one goes to negative infinity. So dysfunction goes to negative infinity when a goes to two So this integral is tavern and

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