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

question 208

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].
- $f ( x ) = 5 x ^ { 2 } + 4$ over the interval $[ 0,3 ]$ .

• A) \(12 + \frac { 270 n ^ { 3 } + 405 n ^ { 2 } + 135 n } { 6 n ^ { 4 } }\); Area \(= 12\)
• B) \(12 + \frac { 270 n ^ { 3 } + 405 n ^ { 2 } + 135 n } { 6 n ^ { 3 } } ;\) Area \(= 45\)
• C) \(12 + \frac { 270 n ^ { 3 } + 405 n ^ { 2 } + 135 n } { 6 n ^ { 4 } } ;\) Area \(= 57\)
• D) \(12 + \frac { 270 n ^ { 3 } + 405 n ^ { 2 } + 135 n } { 6 n ^ { 3 } } ;\) Area \(= 57\)

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