# Thread: Left and Right Hand Rules

1. $\{(4 * 7^2 + 2 * 7 + 4) * 2\} + \{(4 * 9^2 + 2 * 9 + 4) * 2\} + \{(4 * 11^2 + 2 * 11 + 4) * 2\} =$

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

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

$2(214 + 346 + 510) =$

$2(1070) = 2140.$

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

3. Originally Posted by tennisman123
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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