Integrate the following values of y from x = 0 to x = 130 using (a)...

Integrate the following values of y from x = 0 to x = 130 using (a) The midpoint rule using intervals of [0 10], [10 30], [30 70], and [70 130] (b) The trapezoid rule using the same intervals (c) Simpson’s rule using the same intervals

x y

0 6

5 12

10 18

20 30

30 42

50 36

70 24

100 18

130 6

Integrate the differential equation dydt = y from t = 0 to t = 1 in one step (i.e., with a t of 1) using the Euler method, the Improved Euler method, and the classical Runge-Kutta method, which is the analog of Simpson’s rule. Assume that the initial value of y is 1. Compare your answers to the correct answer, which is exp(1) = 2.7183. You can do all the calculations with an excel spread sheet. Alternatively, you can do all the calculations by hand.

Expert Solution

By dividing the interval and using formula for each method we can find the result.

orchestra answered 2 years ago

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