Integrate the following function both analytically (you may want to use an online integral calculator or a table of integrals) and numerically: I(f)=0115xdx a) ( 5 points) Analytical b) (10 points) Trapezoidal rule c) ( 10 points) Simpson's 1/3 rule d) (15 points) Simpson's 3/8 rule Calculate all values to exactly seven decimal points. For all numerical cases, start with n=2, then double the number of segments until your last computation includes 512 segments. Compute the percent relative errors, out to exactly four decimal points, for the numerical results (as compared to the analytic answer). %Error=AnalyticAnswerNumericalAnswerAnalyticAnswer Provide a formatted table showing the value of the integration and its error for each value of n. Hint: Create a loop on ' n, doubling its value each time through the loop. Table should look like the following: Table should look like the following