Question

Do the following with the given information. $$ \int_{0}^{1} 39 \cos \left(x^{2}\right) d x $$ (a) Find the approximations $$ T_{8} $$ and $$ M_{8} $$ for the given integral. (Round your answer to six decimal places.) $$ T_{8}= $$ $$ M_{8}= $$ (b) Estimate the errors in the approximations $$ T_{8} $$ and $$ M_{8} $$ in part (a). (Use the fact that the range of the sine and cosine functions is bounded by $$ \pm 1 $$ to estimate the maximum error. Round your answer to seven decimal places.) $$ \left|E_{T}\right| \leq 0.3046875 $$ Awesome! $$ \left|E_{M}\right| \leq 0.15234375 $$ Nice work! (c) How large do we have to choose $$ n $$ so that the approximations $$ T_{n} $$ and $$ M_{n} $$ to the integral are accurate to within 0.0001? (Use the fact that the range of the sine and cosine functions is bounded by $$ \pm 1 $$ to estimate the maximum error.) $$ n \geq 442 $$ for $$ T_{n} $$ $$ n \geq 313 $$ for $$ M_{n} $$

          Do the following with the given information.
$$ \int_{0}^{1} 39 \cos \left(x^{2}\right) d x $$
(a) Find the approximations $$ T_{8} $$ and $$ M_{8} $$ for the given integral. (Round your answer to six decimal places.)
$$ T_{8}= $$
$$ M_{8}= $$
(b) Estimate the errors in the approximations $$ T_{8} $$ and $$ M_{8} $$ in part (a). (Use the fact that the range of the sine and cosine functions is bounded by $$ \pm 1 $$ to estimate the maximum error. Round your answer to seven decimal places.)
$$ \left|E_{T}\right| \leq 0.3046875 $$ Awesome!
$$ \left|E_{M}\right| \leq 0.15234375 $$ Nice work!
(c) How large do we have to choose $$ n $$ so that the approximations $$ T_{n} $$ and $$ M_{n} $$ to the integral are accurate to within 0.0001? (Use the fact that the range of the sine and cosine functions is bounded by $$ \pm 1 $$ to estimate the maximum error.)
$$ n \geq 442 $$ for $$ T_{n} $$
$$ n \geq 313 $$ for $$ M_{n} $$

do the following with the given information int01 39 cos leftx2right d x a find the approximations t8 and m8 for the given integral round your answer to six decimal places t8 m8 b estim 52202

Added by Melissa G.

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