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Numerade Educator

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Problem 24 Medium Difficulty

Repeat Exercise 23 for the integral $ \displaystyle \int_{-1}^1 \sqrt{4 - x^3}\ dx $.

Answer

a. $\left|f^{\prime \prime}(x)\right| \leq 5$
b. Midpoint rule approximation is 3.9958041521928
c. Error bound is 0.0066
d. 3.99549 using Simpson's Rule with $n=50$
e. Actual error is less than that found in part (c)
f. $f^{\prime \prime \prime \prime}(x)$ is bounded between $-0.2$ and $-0.4$ in $(-1,1)$
g. Simpsons rule approximation with $n=10$ is 3.9954497901518
h. Error bound is 0.000007111111
i. Actual error in approximation is more than the theoretical error calculated
j. n should be 712 or more for the simpsons approximation to have an error less than 0.0001

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Video Transcript

Okay, problem. 24. The point is how to do that part problem? Not a crackdown, sir. You know. So let me teach you how to do that. Yeah. The 1st 1 is use a graft to get a good upper bond for the second director of that. What is that at this? This one. So he used, uh, self. Their name Mathematica. There, this big second director, um, off it it is. We can find out when, Actually, it's you tickle toe one. It has the Mexico by there. So I think the maximum value is 2.17 actually, but the answer is fire. I don't know why there's a five here. Okay, That's not important. Just, uh, just hold onto it. That matters, right? Used am 10 in. You need to know how to find an antenna. Here's a rule. You know everything in the formula. Just use it. Just use a formula you can compute and 10 right. Used party to ask him. It's our estimates era. You need another formula here. Yeah. Hey, is the upper balling up that right? And the A, I don't know, just used it. Just use it. I don't know whether the South ridge crack here. You can make a Your aunt tried to believe it or not. And four use a beauty. Oh, you need thio. Approximate I on my calculator. You need a calculator? Yeah. McCarroll heard the answer is 3.995 or 87 safe. 77 You need a calculator? Yeah. How does the actual era? What is extra era, Dr O'Hara? It's just I minus, uh, the thing, right. You know, I'm 10. I just that you know, I and you know, Hampton, just compute. Just compare it with the ass to me. Yeah, I'm right. I think it is much, much smaller than the estimate. Use a graft. Got a boot up her bond. Paul. The force structure that's begin? Yes. Tonight for here's oh, Carrie Hiss so we can find out when practicing with one. The options have Mexico, right? Just compute it. You know the doctor? It is this wanting to this, uh, fine one, right? Use Aston. There's no how to compute Astor. Person is just used a Simpson or the formula here. Uh, I daresay our days knowing, you know, just compute. Just calculate there's no trick here. His partner, after asking with Sarah harassment to me, is that Sarah, you need to know this function. You know this former Hayes? Ah, upper bone of the fourth directive of that just computed and just compare it. I'm just saying collection and B. Yeah, you need to. That's great. And the other one? Okay, Times B minus a you to the fifth, ready by 180. And to the forest is wondered. And 0.1 Yes. Solve this question. Equality and you can get it. And this greater than blood. I don't know whether the author is cracked or not. So that's that problem is quite easy by these complex off course, you need to Technically, you need a lot of speculation, right? Great.