Question

Help pls AP CALCULUS!

Answer 1

9

Explanation:

Let first find the width of the subintervals

`(4 - 0)/(4) = 1`

We are using MRAM, so we will be using the midpoint interval height as the height.

So for the first rectangle

The midpoint of interval [0,1] is 0.5

The midpoint of the second interval [1,2]=1.5

The midpoint of the third interval [2,3]=2.5

The midpoint of the fourth interval [3,4]= 3.5

So let's set up an equation

Using Riemann sums, we are adding up rectangle areas so we will use the midpoint height (since we are using MRAM) and delta x(which is 1)

`r = f(0.5)(1) + f(1.5)(1) + f(2.5)(1) + f(3.5)(1)`

We will then get an area of

`9`

That is the approximate area.

The real area is 9.333333, so this is close somewhat.

The answer is 9