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anonymous
 5 years ago
trapezoidal rule n=6 integral upper integral pi lower 0 {cos(x/2) dx
anonymous
 5 years ago
trapezoidal rule n=6 integral upper integral pi lower 0 {cos(x/2) dx

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[\int\limits_{0}^{\pi}\cos (x/2) dx\]

Yuki
 5 years ago
Best ResponseYou've already chosen the best response.0if you want to use the trapezoidal rule, all you are trying to do is to estimate the area under the curve cos(x/2) using 6 trapezoids.

Yuki
 5 years ago
Best ResponseYou've already chosen the best response.0so that each height of the trapezoids are pi/6

Yuki
 5 years ago
Best ResponseYou've already chosen the best response.0since the area of a trapezoid can be calculated by the formula 1/2(b_1+b_2)h, all you have to do now is to find out b_1 and b_2 in each trapezoid.

Yuki
 5 years ago
Best ResponseYou've already chosen the best response.0for the left most trapezoid, b_1 will be the left base, which can be calculated by cos(0/2) = 1. b_2 would be the right base an similarly can be calculated by cos(pi/6 /2) = not a nice number. the height of the trapezoid was h = pi/6, so the area is 1/2 ( 1 + cos(pi/12))*pi/6.

Yuki
 5 years ago
Best ResponseYou've already chosen the best response.0the next trapezoid will have b_1 which is cos(pi/12). As you noticed, it is the same as the b_2 for the first trapezoid. They have to be the same because they share that side.

Yuki
 5 years ago
Best ResponseYou've already chosen the best response.0Anyway, b_2 for the second trapezoid would be calculated by cos( 2*pi/6 /2) because now the x value you are plugging in is 2*pi/6.

Yuki
 5 years ago
Best ResponseYou've already chosen the best response.0the height is the usual, pi/6 so the area of the second trapezoid would be 1/2 (cos(pi/12) + cos(pi/6)) * pi/6

Yuki
 5 years ago
Best ResponseYou've already chosen the best response.0you keep doing this until you get the 6 trapezoids :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0to do simpsons rule same problem it will be aprox the same answer correct?

Yuki
 5 years ago
Best ResponseYou've already chosen the best response.0yes, but instead of a trapezoid, now you will be using a quadratic. good luck :)
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