Math: Need Answer to study for a quizz. Help ASAP
posted by Jesse
Estimate the area under the curve f(x)=x^24x+5 on [1,3]. Darw the graph and the midpoint rectangles using 8 partitions. Show how to calculate the estimated area by finding the sum of areas of the rectangles. Find the actual area under the curve on [1,3] using a definite integral.

drwls
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 graphdrawing 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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