1. We consider approximating fol H1352 dm : :5 0.785... The second derivative is 2 (33:2 1) f"($) : (I2+1)3 ) with the graph of | f" ($)| plotted below. (a) apczold Rule (Use a calculator as appropriate) i. Use the Trapezoid Rule to approximate this integral, with n = 4. ii. Estimate the error in this approximation. iii. Verify that your approximation is within the error estimate you obtain. iv. Determine the value of n such that the approximation is accurate to within 0.0001. (b) Midpoint Rule {Use a calculator as appropriate) i. Use the Midpoint Rule to approximate this integral, with n : 4. ii. Estimate the error in this approximation. iii. Verify that your approximation is within the error estimate you obtain. iv. Determine the value of n such that the approximation is accurate to within 0.0001