Question

In each of the options, A, B and C

below, a different number of strips
have been used to estimate the area
under the curve.
b) Use the option you chose in part a)
to estimate the area under the curve.

a) Which option gives the best
estimate?

Answer 1

The best estimate for the area under a curve in mathematics is obtained by using the most number of strips, as more strips provide a better approximation. For the right triangle mentioned, the area is calculated as half the base times the height.

Step-by-step explanation:

The question involves estimating the area under a curve, which is a concept from integral calculus in mathematics. The area can be estimated using different numbers of strips or rectangles under the curve; the more strips used, the better the approximation of the area. Therefore, option A which uses the most strips would likely yield the best estimate for the area under the curve.

To estimate the area under the curve as described in the question, you would measure the height of each strip (how high the curve is at each point) and multiply it by the width (distance) that each strip covers.

Then, by summing up all the areas of these strips or rectangles, you can approximate the total area under the curve. For a right triangle, as mentioned in option B, the area is ½ × base × height.