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The Answer Key

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1万 回視聴 ・ 89いいね ・ 2020/08/06

Find an expression for the area under the curve y=x^(3) from 0 to 2 as limit. Use following formula

(a) Use the following definition to find an expression for the area under the curve y = x3 from 0 to 2 as a limit.
The area A of the region S that lies under the graph of the continuous function f is the limit of the sum of the areas of approximating rectangles:
A =
lim
n → ∞
Rn =
lim
n → ∞
[f(x1)Δx + f(x2)Δx + . . . + f(xn)Δx]
A =

lim
n → ∞
n

2i
n

·
2
n

i = 2

lim
n → ∞
n

2i
n
3

·
2
n

i = 2


lim
n → ∞
n

2i
n
3

·
2
n

i = 1

lim
n → ∞
n

2i
n
3

·
2i
n

i = 0

lim
n → ∞
n

2i
n
3

·
2i
n

i = 1
Correct: Your answer is correct.

(b) Use the following formula to evaluate the limit in part (a). .

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