Question

Use three rectangles of equal width and the left endpoint approximation method to estimate the area enclosed by the x-axis, the lines x = 1 and x = 4, and the curve y = x^(1/2).

Could you please help me understand how to do this?

Thanks in advance!

Answer 1

ok, the three rectangles run at x=1, 2, 3 for the left endponits, at y=x^.5
the width is 1, so the area is 1*x^.5

areas:
first 1-2, area=1*1^.5 left endpoint
second 2-3, area=1*2^.5
third 3-4, area=1*3^.5

so the sum of areas is
1+sqrt2 + sqrt3