Chapter 6.1, Problem 6E

To determine

The value of RRAM and MRAM.

Answer to Problem 6E

The area by RRAM is 1.25 and the area by MRAM is 1.375.

Explanation of Solution

Given information:

The graph of the function $y=2x-x^2$ and the x-axis for $0\le x\le 2$

Formula used:

  $\text{Area=}\left(\frac{\text{1}}{\text{2}}\right)\left(\text{height}\right)$

Calculation:

RRAM means right-hand endpoint rectangular approximation method. The name suggests the choice by determining the heights of the approximating rectangles.On evaluating the function at the right-hand endpoint of each subinterval.

  

So, estimated area by RRAM is 1.25.

MRAM means midpoint rectangular approximation method. The name suggests the choice of determining the heights of the approximating rectangles. The function at the midpoint of each subinterval is to be evaluated as follows,

  

So, estimated area by MRAM is 1.375.

Conclusion:

The area by RRAM is 1.25 and the area by MRAM is 1.375.