When using a numerical method to approximate the value of an integral, we expect there to be some discrepancy between the exact value and the value found by our computation. We cannot (usually) determine exactly what this error is, but it is possible to show that the (absolute value of the) error in using the trapezoid rule to approximate f f(x) dx cannot exceed the bound E(n) = (b-a)3³ 12n² -M where M is the maximum value of f"(x)| on the interval [a, b]. (a) Compute √™1² s sin(x) dr. (b) Compute the trapezoid rule estimate of this integral using n = 4 to at least 4 decimal places. (c) State the error in using this approximation; i.e., state the difference between the exact value in (a) and the approximation in (b) to at least 4 decimal places. (d) Find the value of M for this problem. That is, find the maximum value of f"(z)| on the interval [0, where f(x)= sin(z). You may do this by sketching a graph of f"(z)| and determine what the maximum is, or by using calculus techniques. (e) Find the error bound E(n) for approximating * sin(z) dr using Trapezoid rule with n = 4, n= 10, and n = 20. That is, find E(4), E(10), and E(20) to at least 4 decimal places. (f) Find the first value of n which is large enough that the error bound E(n) is smaller than 0.0001.