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First make a substitution and then use integration by parts to evaluate the integral.

$ \displaystyle \int_0^\pi e^{\cos t} \sin 2t dt $

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Calculus 2 / BC

Chapter 7

Techniques of Integration

Section 1

Integration by Parts

Integration Techniques

Campbell University

Harvey Mudd College

University of Michigan - Ann Arbor

Boston College

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.

02:14

First make a substitution …

06:27

Evaluate the integral.

03:25

04:26

10:46

01:01

Evaluate the definite inte…

04:37

04:27

04:10

05:17

00:28

Evaluate the indefinite in…

02:46

Evaluate the integral.…

05:41

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