This problem concerns using numerical methods to calculate the integral                                 Note that the exact value is,  = ( 2 − −2 )/2. (a) Using the composite trapezoidal rule, and 4...

This problem concerns using numerical methods to calculate the integral

Note that the exact value is,
 = (
²
−

⁻²)/2.

(a) Using the composite trapezoidal rule, and 4 subintervals, find an approximate value for the integral. What is the error?

(b) Using the composite Simpson’s rule, and 4 subintervals, find an approximate value for the integral. What is the error?

(c) Using the composite Hermite rule, and 4 subintervals, find an approximate value for the integral. What is the error?

(d) Using the composite trapezoidal rule, how small does the step size
 have to be to guarantee that the numerical error is less than 10⁻⁶?

(e) Using the composite Simpson’s rule, how small does the step size
 have to be to guarantee that the numerical error is less than 10⁻⁶?

(f) Using the composite Hermite rule, how small does the step size
 have to be to guarantee that the numerical error is less than 10⁻⁶?