Check the solution to "The trapezoidal rule applied on ∫ 0 2..."

letumsnemesislh

Answered question

2022-07-10

The trapezoidal rule applied on

\int_{0}^{2} [f (x)] d x

gives the value 5 and the Midpoint rule gives the value

4

. What value does Simpson's rule give?

gozaderaradiox5

Beginner2022-07-11Added 19 answers

First of all,

f (1)

should be

2

since midpoint rule gives you

2 f (1) = 4

. You also know that

f (0) + f (2) = 5

. So

S = \frac{1}{3} [f (0) + 8 + f (2)] = \frac{8}{3} + \frac{1}{3} \cdot 5 = \frac{13}{3}

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