Estimate the error if t6 (trapeziod rule with n=6) was used to calculate ∫30cos(2x)dx.

The error bound for a trapezoid rule is given with this formula:

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:

In order to find K we must find the second derivative of our function:

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:

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.

14 estimated and 13.62 exacti’m pretty sure..