Question

(a) Find the approximations T₈and M₈for the given integral. (Round your answer to six decimalplaces.)

(b) Estimate the errors in the approximations T₈and M₈in part (a). (Use the fact that the range of the sine and cosinefunctions is bounded by

Given 35 cos(x2) dx Find the approximations T8 and M8 for the given integral. (Round your answer to six decimal places.) 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 plusminus 1 to estimate the maximum error. Round your answer to seven decimal places.) 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 plusminus 1 to estimate the maximum error.)