Doug C. answered • 12/03/15
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Hi Leigh,
Each rectangle (there are six of them) has a width of 1. So what needs to happen is to determine the length of each rectangle, multiply by 1 (LW=A) to get its area then sum those six areas. The question is how do we find the length. Based on the picture it looks like the intent is to use the midpoint of each width as the value to supply to the "function" to get the corresponding y-value (or length of the rectangle).
So for the far left rectangle the midpoint of the width is -2.5 (think of averaging -3 and -2).
f(-2.5) will give its y-value, that is f(-2.5) = 4-(-2.5)/1+(-2.5)2 ≈.9 (so the first rectangle has an area of about (.9)(1) = .9.
Do the same for the other 5 rectangles, add the 6 areas together and you have the sum of the areas of the shaded rectangles.
Since your answer is supposed to go to 3 decimal places, you should probably use .897 for the length of that first rectangle.
