The error bound for a trapezoid rule is given with this formula:
[tex]|E_t|\leq\frac{K(b-a)^3}{12n^2}[/tex]
Where n is the number of points we used in the approximation, a and b are starting and ending point of an integral, and K is the number such that:
[tex]|f''(x)|\leq K[/tex]
In order to find K we must find the second derivative of our function:
[tex]f(x)=30\cos(2x)\\ f'(x)=-60\sin(2x)\\ f''(x)=-120\cos(2x)[/tex]
From this, we can see that our K is 120. This is the amplitude of this periodic function.
Now we can calculate the error bound:
[tex]E_t|\leq\frac{120(b-a)^3}{12\cdot6^2}=\frac{120}{432}(a-b)^3[/tex]
Since you did not specify the interval of integration I cannot compute the final error bound. You can simply plug in the numbers to get the answer.
