Question

Riemann sum question:

Answer 1

One of the riemann sums I'm calculating is with 10 intervals. Is this the correct notation?
\[\sum_{0}^{2} 1 + x^3/4\]

Answer 2

no this is much more of a pain than that

Answer 3

I have to rewrite the equation to reflect the 10 intervals?

Answer 4

?

Answer 5

this is really a pain

Answer 6

you have to start with
\[b-a=2-0=2\]and divide this up into 40 intervals, each will have lenght
\[\frac{2}{40}=\frac{1}{20}\]

Answer 7

then you have to write
\[x_0=0,x_1=\frac{1}{20},x_2=\frac{2}{20}, ...,x_k=\frac{k}{20}\]

Answer 8

then compute
\[f(x_k)=1+\frac{1}{4}(\frac{k}{20})^3\]

Answer 9

finally you have to add
\[\Delta x=\frac{1}{20}\]

\[\sum_{k=0}^{40}f(x_k)\Delta x\]
\[\sum_{k=0}^{40}(1+\frac{1}{4}(\frac{k}{20})^3)\frac{1}{20}\]

Answer 10

have fun

Answer 11

this part
\[\sum_{k=1}^{40}1\times \frac{1}{20}\] is not a problem, it is just
\[40\times \frac{1}{20}=2\] it is the rest that is going to suck

Answer 12

lol thanks. I should be able to figure out the others from this info.

Answer 13

\[\frac{1}{4}\sum(\frac{k}{20})^3\times \frac{1}{20}\] is going to be a pain but at least we can pull out the 1/20 and get
\[\frac{1}{80}\sum (\frac{k}{20})^3 then use a summation formula