Question

Evaluate the Riemann sum for (x) = x3 − 6x, for 0 ≤ x ≤ 3 with six subintervals, taking the sample points, xi, to be the right endpoint of each interval. Give three decimal places in your answer.

Answer 1

The riemann sum is defined as:
\[\int\limits_{a}^{b}f(x)dx \iff \lim_{n \rightarrow \infty}\sum_{i=1}^{n}f(a +i(\frac{ b-a }{ n }))(\frac{ b-a }{ n })\]

Answer 2

"n" represents the amount of sub-intervals.
"b" and "a" are the numbers that define the interval.

This is a way to get a good approximation, (of course, you'll have to know some properties of the sumatory).

Answer 3

Ok
Should I set it up? Openstudy glitched and said you were typing so I wanted to see what you had to say first.

Answer 4

like this:
\[\int\limits_{0}^{3}f(x)dx \iff \lim_{n \rightarrow \infty}\sum_{i=1}^{n}f(0+i(\frac{ 3-0 }{ n })).(\frac{ 3-0 }{ n })\]
Notice that here we are taking infinite many divisions, but it'll give you a better approximation than just 8.

Answer 5

i notice it doesnt say that the subintervals have to be the same width each

Answer 6

Ok, but what about the sub intervals?

Answer 7

@amistre64 so how would that work?

Answer 8

divide the interval into 6 parts, and take the value of the function at the rightmost of each subinterval, then add up all the parts.

essentially you are finding that area of 6 rectangles and adding them up