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Problem 31 Hard Difficulty
(a) Use the Midpoint Rule and the given data to estimate the value of the integral $ \displaystyle \int_1^5 f(x)\ dx $.
(b) If it is known that $ -2 \le f^{\prime \prime} (x) \le 3 $ for all $ x $, estimate the error involved in the approximation in part (a).
Answer
a. 14.4
b. $\frac{1}{2}$
Topics
Integration Techniques
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Top Calculus 2 / BC Educators
Catherine R.
Missouri State University
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Watch More Solved Questions in Chapter 7
Video Transcript
problem. 31. You the meat point rule and a human data. Uh, we can't find out that third axes 0.5. But if you want to use the me point rule, you need to know, uh, one point to fight, right? But you don't know so that their head, so that the fact is not 3.5 to their next. What on? Only the to this data, This data, this data on distant eyes useful and they were always want. So, uh, dancer is just 1.5 just 2.5. Just this once. Just this one. It's just 2.9 US 3.6 plus four plus 3.9. That's the sex going by plus 7.9. It's just, uh, 14.4. Here's Alyssa 0.4. And if you know that, uh, is where it's oneof this three than K is equal to three. And you can use the the homeowner here. Be minus a is fire minus one. Right. Fire by this one. Times cake hates re Daddy by 24 I square, right? Yes, it is fair. And what is that in this four? Right, Because you divided the whole goingto four pieces. So that's a 12 and two. Ah, that's Ah won over 32 right? That's home.
University of Wisconsin - Madison
Topics
Integration Techniques
Top Calculus 2 / BC Educators
Catherine R.
Missouri State University
Anna Marie V.
Campbell University
Kristen K.
University of Michigan - Ann Arbor
Michael J.
Idaho State University