Evaluate The Integral (integrate x^2 cos(mx) dx) Integration By Parts Two Times In One Problem скачать в хорошем качестве

Evaluate The Integral (integrate x^2 cos(mx) dx) Integration By Parts Two Times In One Problem

Evaluate the integral (integrate x^2 cos(mx) dx) Integration by parts two times in one problem | Jake's Math Lessons Evaluate the integral (integrate x^2 cos(mx) dx) Integration by parts two times in one problem | Jake's Math Lessons Integration by parts is a very common type of problem that you'll have to be familiar with when you're learning about calculus. And in one of my weekly live streams that I did recently, which I'm doing every Monday night at 5 o'clock Pacific, I went over how to integrate the ∫ x^2cos(mx)dx And this is a pretty interesting example. So I wanted to show you the portion of that live stream where I went over that problem because not only is this a good example of how to apply integration by parts, but it's also a great example of what it looks like when you have to do integration by parts two times in one problem, which makes it kind of challenging but also pretty interesting. So without further ado, let's go ahead and jump right into the example and I'll show you what I'm talking about. We are going to evaluate the integral ∫ x^2cos(mx)dx So in this case, m is we're going to treat as an unknown constant. So this is not a variable, it's just a constant. Basically this would be the same as saying like the integral of x^2*cos4x or x^2*cosπx or whatever, 'm' is just going to be some unknown constant. Again, same kind of process like we did in the last example. The first thing we need to do, first step of any integration by parts problem is to just figure out what do you want to make 'u' and what do you want to make dv? So this is really not too different from the last example we did because again, if you have sin or cosine, usually it doesn't really matter whether you take the derivative or the anti derivative. The derivative of sin and cosine, or the anti derivative of sin and cosine, they only differ from each other by a constant. So if we're taking the derivative of this term or the antiderivative, it's not really going to be any less or more complicated. It's just going to differ by a constant which when you're integrating, you can just pull the constant out of the integral, which means it's really going to make no difference in the integration process. However, Lets Go through the whole problem how I discuss here. I hope you will understand the method of solving such problems. Chapters 0:00 Introduction 0:48 The Problem 2:04 Derivative of x^2 4:26 Finding du and v 5:56 Check My Integral Calculus Cheat Sheet 15:47 Solve For The Problem YOU MIGHT ALSO BE INTERESTED IN... Download my FREE calculus 1 study guide - https://jakesmathlessons.com/Calculus... My Complete Calculus 1 Package - https://jakesmathlessons.com/complete... Get my calculus 2 study guide - https://jakesmathlessons.com/calculus... Work with me! - Come to Wyzant for some 1-on-1 online tutoring with me and get a $40 tutoring credit for FREE - https://is.gd/cqeuOv Some links in this video description may be affiliate links meaning I would get a small commission for your purchase at no additional cost to you. #jakes_math_lesson #integration_by_parts