When the area under f(x) = x2 + x from x = 0 to x = 2 is approximated, the formulas for the sum of n rectangles using left-hand endpoints and right-hand endpoints are as follows. Left-hand endpoints:      SL =  14 3 −  6 n +  4 3n2 Right-hand endpoints:      SR =  14n2 + 18n + 4 3n2 Use these formulas to find SL(12) and SR(12). (Round your answers to two decimal places.) SL(12)  =    SR(12)  =

Advanced Engineering Mathematics
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Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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When the area under

f(x) = x2 + x from x = 0 to x = 2

is approximated, the formulas for the sum of n rectangles using left-hand endpoints and right-hand endpoints are as follows.

Left-hand endpoints:      SL
14
3
 − 
6
n
 + 
4
3n2
Right-hand endpoints:      SR
14n2 + 18n + 4
3n2

Use these formulas to find SL(12) and SR(12). (Round your answers to two decimal places.)

SL(12)  =   
SR(12)  =   
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