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Make the given changes in the indicated examples of this section and then solve the resulting problems.In Example $3,$ change $n$ from 10 to 5 .

Calculus 1 / AB

Chapter 25

Integration

Section 5

Numerical Integration: The Trapezoidal Rule

Integrals

Campbell University

University of Michigan - Ann Arbor

Idaho State University

Lectures

03:09

In mathematics, precalculu…

31:55

In mathematics, a function…

01:19

Solve each problem. See Ex…

01:27

04:39

Solve. See Examples 4 and …

00:45

Watch the section lecture …

01:43

Solve each equation. Check…

03:29

Solve each equation. Choos…

00:43

Solve. See Examples 1 thro…

00:53

04:07

Decide if each statement i…

00:25

we will approximate the value of the interval from 2 to 3 of x times square root of x plus one. By the trap aside the rule With five serve intervals. So first let's define the function F of x equals X times square root of X plus one which is the integral. And we define that function on the closed interval 23. And with that we calculate now the step size age which is the common distance between any two consecutive notes And is the length of the interval of integration 3 -2 over the numbers of intervals here considered which is five And this gives us 1/5, That is 0.2. With that we now determine the notes we get to use and these are it's not equal two ex want equal 22 X two equal 2.4 X three equal 2.6 X four equal 2.8 And X five is the last note equal three. These are the knows we've got to use and with this we can say that the interval from 2 to 3 of x times squared of X plus one Is approximately equal to T5. That is a trap. So the rule with five serve intervals which is the finest age. Half times the image of the first note. X note plus two times the image of the second note plus two times the image of the third note, Last two times the image of the 4th note Plus two times the image of the fifth note and plus the image of the last note which is X five. Remember here is X four. Just put it correctly. Okay so this is a formula of trump's of the rule with five of intervals. And this give us equal to Ages 0.2 That over two times F at two last two F At 2.2 Plus two f. at 2 4 Plus to have a 2.6 plus To have a 2.8 Plus F. at three. And is equal to 0.1 times. The image attending note is next time squared of X plus one. So it's for F for X equal to yet To score 2 3 plus. Uh We have this factor to out and The image is 2.2 square root of 2.2 plus one. So it's two times 2.2 will be 4.4 squared off 3.2 plus two times. Sorry, just put the result. These two times 2.4 is 4.8 Squared off, 3.4. Last two times 2.6. It's 5.2 squared off. Okay, that's pretty. You do better. 52 square it off. Uh 2.6 plus one is three 0.6 plus. Then we have two times 2.8. 5.6 Squared off. two plus 1 is 3.8 plus three sq- four. That is we can But the result here is 2 3 times to six. Okay, so you have this now uh in this moment we gotta use a calculator. And we have used that. We have you used a calculator and we found that disease. Uh This is opportunity equal to four point 69685 3954 084 95 seven. It is the integral from 2 to 3 of X times square root of X plus one separate, ultimately equal to four point 69685 395 for 084 957, which was calculated using traps. So the rule with five sub intervals and this Approximations of the interval, you've got to be less accurate than that found in example three. Because there uh We use tens of intervals, but here we are using less of intervals. We're using 5 76.

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