Given. 1 23 cos(x2) dx
integral. gif
0
Do the following.
(a) Find the approximations T8 and M8 for the given integral. (Round your answer to six decimal places.)
T8 =
M8 =
(b) Estimate the errors in the approximations T8 and M8 in part (a). (Use the fact that the range of the sine and cosine functions is bounded by ±1 to estimate the maximum error. Round your answer to seven decimal places.)
|ET| ≤
|EM| ≤
(c) How large do we have to choose n so that the approximations Tn and Mn to the integral are accurate to within 0.0001? (Use the fact that the range of the sine and cosine functions is bounded by ±1 to estimate the maximum error.)
n ≥ for Tn
n ≥ for Mn