Find a Formula for the Riemann Sum Obtained by Dividing $\mathrm { c } _ { \mathrm { k } }$

question 34

Multiple Choice

Find a formula for the Riemann sum obtained by dividing the interval [a, b] into n equal subintervals and using the right-hand endpoint for each $\mathrm { c } _ { \mathrm { k } }$ . Then take a limit of these sums as $\mathrm { n } \rightarrow \infty$ to calculate the area under the curve over [a, b].
- $f ( x ) = 3 x + 6$ over the interval $[ 0,3 ]$ .

• A) \(18 + \frac { 27 n ^ { 2 } + 27 n } { 2 n ^ { 2 } }\); Area \(= \frac { 63 } { 2 }\)
• B) \(18 + \frac { 24 n ^ { 2 } + 28 n } { 2 n ^ { 2 } } ;\) Area \(= 30\)
• C) \(18 + \frac { 27 n ^ { 2 } + 27 n } { 2 n ^ { 2 } }\); Area \(= \frac { 63 } { 5 }\)
• D) \(18 - \frac { 27 n ^ { 2 } + 27 n } { 2 n ^ { 2 } }\); Area \(= \frac { 9 } { 2 }\)

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