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Find the integrals of the functions.$$\sin x \sin 2 x \sin 3 x$$

Calculus 2 / BC

Chapter 7

Integrals

Section 3

Methods of Integration

Integration Techniques

Campbell University

Baylor University

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.

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Find the integrals of the …

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Evaluate the integrals.

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Evaluate the integrals…

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Find the following integra…

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Evaluate the integral.…

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Find the indefinite integr…

number six. And which we need to integrate cynics assigned to it and saying three X. Okay. Now let us just look at this. We have formula and trigonometry that sign X. Same way my next line way equal to one by two because x minus way minus one minus cause X plus Y. Because expressway. So let us plug in here. It will become equal to one by two. Let us take outside because X minus. Well that x minus two. It's which is minus X minus cause three X. And country X. Okay, centric and deer. Okay, so so this Bill Burton has one by two. One by two cost minus X. Is always cause that's simple. So core sex in to sign three X minus because the X sci fi IX here. No, by using this formula for Kazaks cynics process. Uh say next. So we have formula for this. If we of cynics cause why equal to one by two an expressway sign X plus Y. And blessing explains why. So this will be comical. 21 by two. This is sin exports were so by using this integration but using this formula will be getting one by two Sine X plus Y. So sign four X. Yes sign X minus Y assigned to it. Time to act. Yes. Similarly here it will be when it's one by two. Uh same six X less. Fine zero. Okay, so this will become dx Yeah, let us take one by two comments from all this. It will be on by four and science forex assigned to x minus and six X. MDX This one by four. Integration of Science for X days. Integration of Science for X is minus cause four X by four minus because two X by two and plus for 66 by 30. Let's see. Okay so answer will be 22. If we write it properly one by four, then cost six x one by 6.66 minus one by four cost four x miles one by two past two X plus Sleep. They should be the innocent. Thank you.

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