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Use (a) the Midpoint Rule and (b) Simpson's Rule to approximate the given integral with the specified value of $ n $. (Round your answers to six decimal places.) Compare your results to the actual value to determine the error in each approximation.

$ \displaystyle \int_0^\pi x cos x\ dx $ , $ n = 4 $

a.$M_{4} \approx-1.945744, \quad$ error $\approx-0.054256$b.$S_{4} \approx-1.985611, \quad$ error $\approx-0.014389$

Calculus 2 / BC

Chapter 7

Techniques of Integration

Section 7

Approximate Integration

Integration Techniques

Harvey Mudd College

University of Michigan - Ann Arbor

University of Nottingham

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Okay, Problem sakes. You need a calculator to calculate this. First you need to catch this guy, Isaac. Go to minus two. And And if you go too far so you decided the intro into four pieces. Uh, this is or pie. This is tour pie. This is Bye. This is pie, right? And if you want to calculate an a mystical toe, the tirade. Ah, this point just this point at this point. But that that seems, uh, into all the leads up into Roy's by over or after a calculation, because find a and it's equal to minus 1.94544 uh, s what he's asked, the tax is pi minus zero, divided by four. So his pi work for and at zero is zero x four is hi eggs. That's one is ah, power for an X three is high over three times pi over four, right? Just technically everything. And you can get acts. It's equal to one minus 1.9 a 56 I Why? What as era e m is people toe I minus on this calculate, right? Ah, yes. He's got to go. I minus. That's that's all

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