# Thread: Trapezoidal Rule Problem

1. ## Trapezoidal Rule Problem

$\int_{0}^{1}13\cos(x)^{2} dx$

n = 4

values of intervals

are $y_{0} = 13$

$y_{1} = 12.9997525$

$y_{2} = 12.99901002$

$y_{3} = 12.99777261$

$y_{4} = 12.996040$

change in $x = \dfrac{b - a}{n} = \dfrac{1 - 0}{4} = 1/4$

By the trapezoidal rule

$\dfrac{change-in-x}{2}(y_{0} + 2(y_{1}) + 2(y_{2}) +2(y_3}) + y_{4})$

I got 12.998638 (rounded to 6 decimal places but this is wrong.

2. ## Re: Trapezoidal Rule Problem

Well, you can technically pull the 13 out to do the approximation first, and multiply it back in later on.
But the thing is, is it cos(x^2) or cos^2(x)?

3. ## Re: Trapezoidal Rule Problem

Actually I realized what the problem is now: you are supposed to use radians, not degrees.
Always switch your mode to radians for calculus.

4. ## Re: Trapezoidal Rule Problem

You have your calculator in "degree mode" when you should be using radians.