Do the following with the given information.
\int_0^1 27cos(x^(2))dx
(a) Find the approximations
T_(8)
and
M_(8)
for the given integral. (Round your answer to six decimal places.)
T_(8)=,✓ Great work.
M_(8)=,✓ Great jobt
(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
!=1
to estimate the maximum error. Round your answer to seven decimal places.)
|E_(T)|<=
|E_(M)|<=
q,
q,
(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
-1
to estimate the maximum error.)
n>=
q,
\times
for
T_(n)
n>=
◻
\times
for
M_(n)
Do the following with the given information.
\int_0^1 27cos(x^(2))dx
(a) Find the approximations
T_(8)
and
M_(8)
for the given integral. (Round your answer to six decimal places.)
T_(8)=,✓ Great work.
M_(8)=,✓ Great jobt
(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
!=1
to estimate the maximum error. Round your answer to seven decimal places.)
|E_(T)|<=
|E_(M)|<=
q,
q,
(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
-1
to estimate the maximum error.)
n>=
q,
\times
for
T_(n)
n>=
◻
\times
for
M_(n)