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

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) (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(52794) (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 (!)

RELATED QUESTIONS
Which of these values for the number of ounces in a pound is most accurate, when compared (answered by MathLover1)
How does the width of the rectangles used to approximate area under a curve affects the... (answered by stanbon)
Which of the following statements concerning the standard normal curve is/are true (if... (answered by ikleyn)
Which of the following statements concerning the standard normal curve is/are true (if... (answered by robertb)
Which of the following statements concerning the standard normal curve is/are true (if... (answered by oscargut)
suppose you estimate the area under a curve using inscribed rectangles and then estimate... (answered by robertb)
What portion of the area under a normal curve is to the left of z=-2.10? (answered by ewatrrr)
Find the following areas under the standard normal curve. Find a z-score such that 8% of (answered by stanbon)
the rear stabilizer of a certain aircraft can be described as the region under the curve... (answered by tinbar)