Use X*(subscript k) as the left endpoint of each sub interval to find the area under the curve y=F(x) over [a,b]
f(x)= x^3 a=2 b=6 __________________
Click the link below for a good explanation of using estimating rectangles. It would be very difficult for someone to teach you how to do this on a forum.
Pauls Online Notes : Calculus I - Area Problem
Recall:
where
Edit: Sorry I used right endpoints even though I said I was using left endpoints! I've corrected it:
Since we're using left end points, we consider:
So, using the formula:
A bit messy but entirely doable. As you can see, right endpoints are usually nicer =|
Yes. First we have to take care of the sums. Then we have to take the limit and then we finally get a numerical answer.
So, things to note about summations:
- (Basically, you can pull out the constant)
Now, looking at that last expression I gave you:
Notice how the summations don't exactly look like the bulleted ones. Let's consider .
Expand it:
which matches our bulleted formula. Basically, we opened up the shorthand notation and rewritten it.
See if you can carry on from here.