Question

Estimate the interval from -2 to 4 of the quantity x^3*dx using 3 subintervals and A) left endpoints, B) right endpoints, and C) midpoints.
How do I set this up to just be evaluating only the values for one type of rectangle under the curve? Is it a matter of what numbers I set xO, x1, x2, and x3 as?

Any and all help is greatly appreciated!

Answer 1

from -2 to 4 has length 6

Answer 2

if you divide it in to 3 parts, each will have length 2

Answer 3

they will be \[-2,0,2,4\] left hand endpoints are \[-2,0,2\] right hand are \[0,2,4\]

Answer 4

Right, but like, what's the formula or method for plugging that in, with a particular orientation to one side or the boxes that would be drawn into the curve? :/

Answer 5

Those left endpoints are the values you use to determine the height of each rectangle.

So at your first left endpoint, x=-2,
The height of that rectangle will be f(-2)=(-2)^3=-8.

So the area of your first rectangle is
A=length*width
A=-8*2

Answer 6

I should have written:
A=height*width

That would have been more appropriate ;) lol