Answer: 318
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Explanation:
Refer to the diagram below. Notice how I've formed 3 rectangles underneath the curve. The term "right Riemann sum" refers to the idea of making each rectangle's upper right corner be on the curve. The upper left corner spills over top, meaning we have an over-estimate going on here.
Simply find the area of each rectangle, and then add up those sub areas. That will get you to the final answer.
Note how we go from x = -1 to x = 5, which is a distance of 5-(-1) = 6 units. Split three ways and each interval is 6/3 = 2 units wide.
If we started at x = -1, then increasing 2 units leads us to x = -1+2 = 1 as the first x input we compute into f(x). This is the height of the first rectangle.
Then 1+2 = 3 is the next input, meaning f(3) is the height of the next rectangle, and so on. We keep going until all rectangles are accounted for.
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You should have these rectangle heights:
when moving from left to right.
They add up to 3+29+127 = 159. Double that to get to the final answer of 2*159 = 318
The formula I'm using is
[tex]\Delta x*(f(x_1) + f(x_2) + \dots f(x_n))[/tex]
where x1,x2,... represents the values 1, 3, and 5. These are the x values plugged into the function to get the corresponding heights (3, 29, 127)
