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Evaluate the integral.

$ \displaystyle \int_{-1}^1 \frac{e^{\arctan y}}{1 + y^2}\ dy $

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$e^{\pi / 4}-e^{-\pi / 4}$

Calculus 2 / BC

Chapter 7

Techniques of Integration

Section 5

Strategy for Integration

Integration Techniques

Missouri State University

Oregon State University

University of Michigan - Ann Arbor

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.

07:31

01:05

Evaluate the integrals.

01:11

Evaluate the integral.…

06:45

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Evaluate:

02:51

Evaluate.$$\int_{0}^{1…

02:41

Evaluate

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Let's do it. Use up for this one. Let's take you to be our tan. Why then, do you look so recall the distributed for the inverse hand function? Then, from there I could come back to this integral rewrite this. So that's just either the u and then this remaining piece over here. Let's just do it. So here, I don't need a denominator. You do you? So this corresponds to this. And then this corresponds to this Due to this over here, the last thing to do before we integrate is to find the new limits. So here, plug in negative one. And for why? So we have our ten negative one. That's negative. Pyro for and then similarly for the upper limit ten inverse. A positive one is positive power for So these are limits. So integrate that get you to the U. Here are your end points and then just subtract. And that's your final answer.

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