Posted by Jesse on Thursday, November 18, 2010 at 7:35pm.
The actual area is the integral of the f(x) function with x going from 1 to 3.
That is the value of x^3/3 -2x^2 +5x at x=3 minus the value at x=1.
Area = [9 - 19 + 15]-[1/3 - 2 + 5]
= 5 - 3 1/3 = 1 2/3
You will have to do the graph-drawing and numerical approximations to the integral yourself. Break the interval into eight rectangles. The width of each rectangle will be 1/4, and the height will be f(x) at the leading value of x.
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