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Make the given changes in the indicated examples of this section and then solve the resulting problems.In Example $1,$ change $n$ from 4 to 2.
Calculus 1 / AB
Chapter 25
Integration
Section 5
Numerical Integration: The Trapezoidal Rule
Integrals
Missouri State University
Harvey Mudd College
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Lectures
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In mathematics, precalculu…
31:55
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Watch the section lecture …
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Solve. See Examples 1 thro…
00:34
Solve each equation. Write…
01:14
In the following exercises…
01:07
Solve each formula for the…
02:43
To review the six problem-…
04:34
Solve each equation.$\…
00:29
Answer each question. See …
Let's approximate value of the interval from 1-3 of one of our X by the Trump side the rule with to serve intervals so that's in this case is uh modification of the example, one of the textbook and in that example the numbers of intervals used was for in this modification we're gonna use to serve interests but danger is the same. So let's find first the function of of x equal one over X and it is defined Only close interval 1, 3. Their definition is well defined and continues because Zira is not in this interview. Okay, so let's calculate now the step size age, which is the common distance between any two consecutive notes. And it's defined as the length of the interval of integration 3 -1 over the numbers of intervals considered to in this case And that is to over to equal one. So the step size ages one. And with this we can now determined we charge the notes we got to be using. So the first note zero is one, There is a second note X one which is two And the last note next to is three. So as we can see, we have divided into a one, three into two's of intervals of equal length one and that is determined by three notes 12 and three. And with that we can write the approximation to the integral Between one and 3 of the Function one over X. Let's call that approximation to to which is a trap side the rule with the use of intervals, you know, that's defined as h have times the image of the first note. If not plus the double of the some of the images of the internal notes. There is only one internal node in this case is X one so we get to f at X one Plus the image of the last note X two Then this is equal to 1/2 times Because H is one the image of X notice one plus two f x one which is two plus F at three which is the last node, This is 1/2 times and the image of any value is super cold. So this is 1/1 which is one plus two times The images of two is 1/2 Plus the image of 3: 1/3. Yeah and we calculate this, This is 1/2 times one plus two times one half is one plus one third And there is 1/2 times two plus one third and that is one half times uh six plus 17 3rd and this is finally seven, six or 7/6 which is numerically or tests in decimal notation. I'm going to want to experience that is The interval from 1 to 3 of one over X. Okay, be there is opportunity equal to 7/6 which is equal To 1.16 period and then this is the approximation to the interval found using the trap side the rule with to serve intervals this is less accurate, certain, certainly That the approximation using four or more so of intelligence, so this is the final answer.
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