Use the limit process to find the area of the region between the graph of the function and the xaxis over the given yinterval. g(y) = 4y2 − y3, 1 ≤ y ≤ 3
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1 answer

the area is the limit of the sum of rectangles of height f(x) and width ∆x. That sum is (where ∆x = (31)/n = 2/n)
n
∑ f(n ∆x)*∆x = (4(k*2/n)^2  (k*2/n)^3) * 2/n
k=1
= ∑32k^2/n^3  16k^3/n^4
now use your formulas for sums of powers of k to complete the evaluation. 👍
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answered by oobleck
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