(a) Find the approximations T10, M10, and S10 for

15 sin(x) dx.

0
(Round your answers to six decimal places.)
T10 =
29.75285

Correct: Your answer is correct.
M10 =
30.12372

Correct: Your answer is correct.
S10 =
30.00164

Correct: Your answer is correct.

Find the corresponding errors ET, EM, and ES. (Round your answers to six decimal places.)
ET =
0.24715

Correct: Your answer is correct.
EM =
-0.12372

Correct: Your answer is correct.
ES =
-0.00164

Correct: Your answer is correct.

(b) Compare the actual errors in part (a) with the error estimates given by the Theorem about Error Bounds for Trapezoidal and Midpoint Rules and the Theorem about Error Bound for Simpson's Rule. (Round your answers to six decimal places.)
|ET| ≤
0.387578

Correct: Your answer is correct.
|EM| ≤
0.193789

Correct: Your answer is correct.
|ES| ≤
0.002550

Correct: Your answer is correct.

(c) How large do we have to choose n so that the approximations Tn, Mn, and Sn to the integral in part (a) are accurate to within 0.00001?
n =
623

Incorrect: Your answer is incorrect.
for Tn
n =
440

Incorrect: Your answer is incorrect.
for Mn
n =
18

Incorrect: Your answer is incorrect.
for Sn