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

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

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Calculus 2 / BC

Chapter 7

Techniques of Integration

Section 8

Improper Integrals

Integration Techniques

Campbell University

Oregon State University

Baylor University

University of Nottingham

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…

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Determine whether the inte…

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The problem is you tell me why this integral is convergent where there weren't. If you don't know howto find its anti derivative of this function, you can think about my thereto u substitution. But this question we're kind like you is equal to U until Max Then is he going to you? Squire? And the axe is it got you to you. You Now this nd grow is equal to you You, you over you us, you squire. I will see you. And from well, I'm Tio infinity. We can kinds out you So this is called Chu integral from one to infinity. Two times you over. One pass Useless now by the definition of an improper into your o This is the code to the limit he goes to in planete into girl from one to t The function is who the over one plus you square And this is your coat too, Lim. He goes to vanity and anti derivative of the function One over one plus your square is our tenant. You This is a culture too. Terms, lieutenant, you from one two You this you come too. Two hams. Our tenant You minus ten in one. That's what he goes to infinity. I've tended to you goes too high over to answer if you come too. Two towns. I already too minus octane in one. If we go too Hi over, for his answer is you go to hi Over two this integral has converted and the value is high over too.

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