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Use the Trapezoidal Rule and Simpson's Rule to approximate the value of the definite integral for the given value of n. Round your answer to four decimal places and compare the results with
the exact value of the definite integral.
+9 dx, n = 4
p(500)
Exact
Trapezoidal
Simpson's
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-3 points LarCalcET6 5.6.006.
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Use the Trapezoidal Rule and Simpson's Rule to approximate the value of the definite integral for the given value of n. Round your answer to four decimal places and compare the results with
the exact value of the definite integral.
Trapezoidal
Simpson's
√x dx,
n = 8
exact
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Use the Trapezoidal Rule and Simpson's Rule to approximate the value of the definite integral for the given value of n. Round your answer to four decimal places and compare the results with
the exact value of the definite integral.
Trapezoidal
Simpson's
*(-3-x²) dx, n=6
exact
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-13 points LarCalcET6 5.6.010.
My Notes Ask Your Teacher
Use the Trapezoidal Rule and Simpson's Rule to approximate the value of the definite integral for the given value of n. Round your answer to four decimal places and compare the results with
the exact value of the definite integral.
x²+1
2 dx, n = 4
Trapezoidal
Simpson's
exact
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-13 points LarCalcET6 5.6.012.
My Notes Ask Your Teacher
Approximate the definite integral using the Trapezoidal Rule and Simpson's Rule. Compare these results with the approximation of the integral using a graphing utility. (Round your answers to
four decimal places.)
Trapezoidal
Simpson's
graphing utility
dx,
n = 4
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Approximate the definite integral using the Trapezoidal Rule and Simpson's Rule with n = 4. Compare these results with the approximation of the integral using a graphing utility. (Round your
answers to three decimal places.)
25x
Trapezoidal
5xe x dx
2.6837
Simpson's
2.9652
Graphing utility
2.9700
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3/4 points | Previous Answers LarCalcET6 5.6.044.
The table lists several measurements gathered in an experiment to approximate an unknown continuous function y =
x 0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00
y 4.28 4.35 4.80 5.50 6.32 7.13 7.81 8.23 8.27
(a) Approximate the integral
S² f(x) dx
using the Trapezoidal Rule and Simpson's Rule. (Round your answers to three decimal places.)
Trapezoidal Rule 12.604
Simpson's Rule
12.604
My Notes Ask Your Teacher
f(x).
(b) Use a graphing utility to find a model of the form y = ax3 + bx² + cx + d for the data. Integrate the resulting polynomial over [0,2] and compare the result with the integral from
part (a). (Round your coefficients to four decimal places.)
y = -1.3431x3+3.9794x2.5861x+4.2679 ×
dx = 12.604
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