Question 01 (e)
Short Problem. Show your work. No credit will be given for the answer without the correct accompanying work.
Consider the Trapezoid Rule for making numerical approximations to .
The error for the Trapezoid Rule satisfies , where for . If for , find a value of to guarantee the Trapezoid Rule will give an approximation for with absolute error, , less than .
Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you?
If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it!
What should , , and be in the Trapezoid Rule?
Checking a solution serves two purposes: helping you if, after having used the hint, you still are stuck on the problem; or if you have solved the problem and would like to check your work.
First, we have , so and thus in the Trapezoid rule formula. Also, from the integral bounds, , and so , and in the formula.
Thus, using the Trapezoid Rule with these values,
Now, find such that