Question

Find the value of the Riemann sumV = sum k = 1 to n f(c_{k}) * Delta*x_{k}

Answer 1

The values for Δx_k are:

`\begin{gathered} (2-0)=2 \\ (3-2)=1 \\ (5-3)=2 \end{gathered}`

So, now we will use the right endpoints of each interval to find the c_k values: 2,3 and 5.

And f(c_k):

`\begin{gathered} 2^2+2=4+2=6 \\ 3^2+2=9+2=11 \\ 5^2+2=25+2=27 \end{gathered}`

So each term in the Riemann sum is:

`\begin{gathered} (6*2)=12 \\ (11*1)=11 \\ (27*2)=54 \end{gathered}`

Adding them together:

`V=12+11+54=77`

The value V is 77.