Consider the integral 3/2 [ x cos(x) dr. (a) Approximate the integral using the mid-point rule...

    

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Consider the integral 3/2 [ x cos(x) dr. (a) Approximate the integral using the mid-point rule with n = 5. Give your answer to 4 decimal places. (b) Approximate the integral using the trapezoidal rule with n = 15. Give your answer to 4 decimal places. (c) Denote the error in your approximations by EM and Er, respectively. By first finding a bound for the second derivative of f(x) = x cos(x2), use the error bounds we have seen in class to bound EM and [ET]. Leave your answers in exact form. (d) What value of n should we choose to guarantee that both the mid-point rule and trapezoidal rule will have error less than 0.01? Consider the integral 3/2 [ x cos(x) dr. (a) Approximate the integral using the mid-point rule with n = 5. Give your answer to 4 decimal places. (b) Approximate the integral using the trapezoidal rule with n = 15. Give your answer to 4 decimal places. (c) Denote the error in your approximations by EM and Er, respectively. By first finding a bound for the second derivative of f(x) = x cos(x2), use the error bounds we have seen in class to bound EM and [ET]. Leave your answers in exact form. (d) What value of n should we choose to guarantee that both the mid-point rule and trapezoidal rule will have error less than 0.01?