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

$ S = \{ (x, y) \mid x \le 0, 0 \le y \le e^x \} $

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Calculus 2 / BC

Chapter 7

Techniques of Integration

Section 8

Improper Integrals

Integration Techniques

Campbell 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.

01:56

Sketch the region and find…

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the problem is catch the region and find it. I am area. Look at this graph. We need to find its area of this part of the safety apart we can use into girl. Um negative Infinity Want zero? The function Each works yaks to denote area off us or this improper integral a definition. This is a call to the limit a goes to make to infinity into girl from a to zero e to axe yaks this's equal Choose limit a goes to make you infinity This is Eagle Tito acts a zero This is a culture of blame It a goes to make to infinity into zero is equal to want minus into eh When a goes to make to you infinity into a goes to zero since answer is the blonde So the area of this region in secret one

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