Estimate the error if t6 (trapeziod rule with n=6) was used to calculate ∫30cos(2x)dx.
1 answer:
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.
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.
You might be interested in
You want the equation for a line that goes through the data points (0, 248) and (5, 277). The slope is ∆y/∆x = (277-248)/(5-0) = 29/5 = 5.8. The first data point is the y-intercept, so your equation in slope-intercept form is
... y = 5.8x + 248 . . . . . . where y is MWh of generation and x is years since 2007.
_____
∆y is read "delta y". It means "the change in y".
