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Sketch the region and find its area (if the area is finite).

$ S = \{ (x, y) \mid -2 < x \le 0, 0 \le y \le \frac{1}{\sqrt{x + 2}} $

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Calculus 2 / BC

Chapter 7

Techniques of Integration

Section 8

Improper Integrals

Integration Techniques

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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.

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Sketch the region and find…

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the problem is sketched and region and find his area. Look at the graph. The region is Shadid here. We need to find the area of this part we can use Integral from next to two zero was a function one over routine exposed to Dean to be not the area of this region. This is an improper, integral a definition. This is the cultures that limit he goes to next year too. Empty girl from tea to zero of the function One over Return Express to Yes. So we've computed a happening The integral first Look at this definite integral. This's kowtow one over on half Juan X class two, two, one of us wass and start, this is negative. One half is ineffective Have plus one from she too. Cyril Simula varieties functions so this is one over half. So this is two Herms X plus to Joe, one half from he to zero on the plugging zero auntie to dysfunction. This's two hams. Two, you are half on minus two hams. He passed too on half power. Now when he goes to negative too, she plus two goes to zero. So this function goes to two. Tough. So when he goes to met, you too says area of this region is two times routes off too.

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