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Evaluate the integral.

$ \displaystyle \int_0^\pi \sin 6x \cos 3x\ dx $

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$\frac{4}{9}$

Calculus 2 / BC

Chapter 7

Techniques of Integration

Section 5

Strategy for Integration

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.

03:59

Evaluate the integral.…

05:52

Evaluate the given definit…

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0:00

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02:03

02:00

01:50

Evaluate the integrals.

03:32

07:01

the first thing we should do here is used this formula on the incident. So in our case, we have a equals six x be evil three x so squat and use this formula zero pie. And then we have signed I necks signed three x and we can evaluate this plug in the end points. So we hear minus negative one over eighteen and then minus and then hear negative one over six and then plug in zero and then go ahead and simplify this. We have won over eighteen one over six, one over eighteen. One of our six couldn't simplify that to be for over nine, and that's a final answer.

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