Left and Right Hand Rules

tennisman123

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(a.)Find the Riemann sum for this integral using the right-hand sums for
n=3
.

(b.) Find the Riemann sum for this same integral, using the left-hand sums for
n=3


I have tried the problem a few times, but i cannot get the right answer. I am getting 3832 for the right hand.. please help
 
View attachment 2360


(a.)Find the Riemann sum for this integral using the right-hand sums for
n=3
.

(b.) Find the Riemann sum for this same integral, using the left-hand sums for
n=3


I have tried the problem a few times, but i cannot get the right answer. I am getting 3832 for the right hand.. please help
I get 2140.

What are the x values you are using? What value for dx?
 
Last edited:
2060 was not correct. the x values i am using are 6,7,8,9,10,11 for the right hand values...
 
its ok. i tried it a few times as is described in the notes, but none of them came out to be correct :/
 
yes its n=3. i also tried 7,9,11 but the answer was not correct. i even multiplied by delta x 2 after adding them together.
 
this is for an online homework problem so the answer does not appear until i get the correct answer.
 
\(\displaystyle \{(4 * 7^2 + 2 * 7 + 4) * 2\} + \{(4 * 9^2 + 2 * 9 + 4) * 2\} + \{(4 * 11^2 + 2 * 11 + 4) * 2\} =\)

\(\displaystyle 2\{(4 * 49 + 14 + 4) + (4 * 81 + 18 + 4) + (4 *121 + 22 + 4)\} =\)

\(\displaystyle 2\{(196 + 18) + (324 + 22) + (484 + 26)\} =\)

\(\displaystyle 2(214 + 346 + 510) =\)

\(\displaystyle 2(1070) = 2140.\)
 
ok i did not multiply everything by 2 before the end. do you know what numbers for the left i would use?
 
ok i did not multiply everything by 2 before the end. do you know what numbers for the left i would use?
With n as three we divide the range over which x is to be integrated into 3 equal parts. The range here runs from 5 to 11. So each dx = 2.

The intervals then are 5 to 7, 7 to 9, and 9 to 11. When we used the right hand rule to evaluate the function being integrated, we chose 7, 9, and 11. If we used the mid-point rule, we would use 6, 8, and 10. So for the left hand rule we use what?
 
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