Question

Estimate the area under the graph of
f(x)=3x^3+5
from x=-1 to x=4, first using 5 approximating rectangles and right endpoints, and then improving your estimate using 10 approximating rectangles and right endpoints.

I'm having problem with using the midpoint to find the area. With 5 rectangle I have 210.625 but I can't figure out how to do the 10 rectangle.

Answer 1

again, you cannot estimate to six significant digits.

on the five rectangle, right endpoints, use 4,3,2,1,0 as right endpoints, width 1

area= f(4)*1 + f(3)*1 + ...

now for ten, use 4, 3.5, 3, 2.5....to -.5, then area width is .5