Left and Right Hand Rules

[tennisman123]

(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

 

[JeffM]

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?

 

[tennisman123]

2060 was not correct. the x values i am using are 6,7,8,9,10,11 for the right hand values...

 

[JeffM]

2060 was not correct. the x values i am using are 6,7,8,9,10,11 for the right hand values...

Sorry I typed too fast. Try 2140

 

[tennisman123]

its ok. i tried it a few times as is described in the notes, but none of them came out to be correct :/

 

[JeffM]

2060 was not correct. the x values i am using are 6,7,8,9,10,11 for the right hand values...

But n = 3, not 6.

7, 9, 11

 

[JeffM]

I'll recheck my arithmetic. I still get 2140.

 

[tennisman123]

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.

 

[JeffM]

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.

What answer does the book give?

 

[tennisman123]

this is for an online homework problem so the answer does not appear until i get the correct answer.

 

[JeffM]

$\displaystyle \{(4 * 7^2 + 2 * 7 + 4) * 2\} + \{(4 * 9^2 + 2 * 9 + 4) * 2\} + \{(4 * 11^2 + 2 * 11 + 4) * 2\} =$

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

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

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

$\displaystyle 2(1070) = 2140.$

 

[tennisman123]

ok i did not multiply everything by 2 before the end. do you know what numbers for the left i would use?

 

[JeffM]

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?