Chapter 5.1, Problem 8E

To determine

To find: The value of PRAM and MRAM.

Answer to Problem 8E

PRAM: $5/4$

MRAM: $11/8$

Explanation of Solution

Given information:

The function is $y=2x-x^2$ for $x\in \left[0,2\right]$

Calculation:

For PRAM, approximate the area under the curve by find the area of each rectangle whose base is $\text{Δ}x=1/2$ and height is the $y$ -coordinate of the function at the right-hand endpoint of its base.

  

Since, the sum of the areas in the LRAM table above approximates the area under the curve $y=2x-x^2$ for $x\in \left[0,2\right]$

Area:

  $\begin{array}{c}=0+3/8+1/2+3/8\\ =\frac{5}{4}\end{array}$

For MRAM, approximate the area under the curve by finding the area of each rectangle whose base is $\text{Δ}x=1/2$ and height is the $y$ -coordinate of the function at the midpoint of its base.

  

Since, the sum of the areas in the PRAM table above approximates the area under the curve $y=2x-x^2$ for $x\in \left[0,2\right]$

Area:

  $\begin{array}{c}=7/32+15/32+15/32+7/32\\ =11/8\end{array}$

Therefore, the required values:

PRAM: $5/4$

MRAM: $11/8$