Please show work!

Give all decimal values rounded to 3 places after the decimal.

2 1.{a} Use the Midpoint Rule with H = 4 subintervals to estimate f 1'2 x. a [b] ICompute the integral exactly. 2. For the integral of problem #1: {3} Use the Error Bound to find the bound for the error. {b} Compute the error made when using this estimate. '9 3.{a) Use Simpson's Rule with rt = 4 subintervals to estimate / if; :11. . 1 (b) Compute the integral exactly. 4. For the integral of problem #3: (3) Use the Error Bound to find the bound for the error. (b) Compute the error made when using this estimate, 10 5. Use the Error Bound formula for the Trapezoidal Rule to determine N so that if f 9 2x dx is approxi- 0 mated using the Trapezoidal Rule with N subintervals, the error is guaranteed to be less than '10 4. 5 6. Estimate f In xdx using the Trapezoidal Rule with H = 6 subintervals. 1 cos2 x 5'. it is a fact, which you can take on faith, that the fourth derivative of x) 2 1 is always less than 2 (in absolute value). Determine N so that '1 2 if f7 H 1 CD: x dx is approximated using Simpson's Rule with N subintervals, the error will be less 0 than 105. Remember that Simpson's Rule requires an even number of subintervals