SOLUTION: Which would give the most accurate estimate of the area under a curve? a. when the region is divided into a greater number of rectangles b. when the region is divided into tw

Algebra ->  Finance -> SOLUTION: Which would give the most accurate estimate of the area under a curve? a. when the region is divided into a greater number of rectangles b. when the region is divided into tw      Log On


   



Question 1180434: Which would give the most accurate estimate of the area under a curve?

a. when the region is divided into a greater number of rectangles
b. when the region is divided into two rectangles
c. when the region is divided into five rectangles
d. when the region is divided into a smaller number of rectangles

Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

answer: a. when the region is divided into a greater number of rectangles
This forms the basics of integration.
Integration can be use to calculate areas under the curve. To find the area under the curve we try to approximate the area under the curve by using rectangles. When we increased the number of rectangles of equal width of the rectangles, a better approximation of the area is obtained. We then find the area of each infinitesimally small rectangle and then integrate by taking two limits, the upper limit and the lower limit.

Answer by ikleyn(52790) About Me  (Show Source):
You can put this solution on YOUR website!
.

It is amazing,  but when you integrate a  LINEAR  function  y = ax + b,

ONE  RECTANGLE is just enough,  if the integration point is selected at the center of the integration region  (!)