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(Solved): \[ \int_{-1}^{1}\left(2 x^{2}+5\right) d x \] 1. Laing the trapercidial raie ...



\[
\int_{-1}^{1}\left(2 x^{2}+5\right) d x
\]
1. Laing the trapercidial raie
a Evirnale the integral with \( n=4 \) steps andThe instructions for the given integral have two parts, one for the trapezoidal rule and one for Simpsors rul
\[
\int_{-1}^{The instructions for the given integral have two parts, one for the trapezoidal rule and one for Simpsons rule
\[
\int_{-1}^II. Using Simpsons rule
a. Estimate the integral with \( n=4 \) steps and find an upper bound for \( \left|E_{S}\right| \).
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\[ \int_{-1}^{1}\left(2 x^{2}+5\right) d x \] 1. Laing the trapercidial raie a Evirnale the integral with \( n=4 \) steps and find an upper bound for \( \left|E_{T}\right| \). \( T=\frac{23}{2} \) (T)pe an exatt answer. Type an integer or a simplified traction.) An upper bound for \( \left|E_{T}\right| \) is 4 . (floure to two decimal planes as needed.) b. Evaluale the zhegral tireclly and find \( E_{T} \). \[ \int_{-1}^{1}\left(2 x^{2}+5\right) d x= \] The instructions for the given integral have two parts, one for the trapezoidal rule and one for Simpsor's rul \[ \int_{-1}^{1}\left(2 x^{2}+5\right) d x \] b. Evaluate the integral directly and find \( \mathrm{E}_{\mathrm{T}} \mid \). \[ \int_{-1}^{1}\left(2 x^{2}+5\right) d x= \] (Type an exact answer. Type an integer or a simplified fraction.) \[ \left|E_{T}\right|= \] (Round to two decimal places as needed.) c Use the formula \( \left(\mid E_{T} /\right. \) (true value) \( ) \times 100 \) to express \( \left|E_{T}\right| \) as a percentage of the integrafs true value. (Round to the nearest integer as needed.) ii. Using Simpsan's rule The instructions for the given integral have two parts, one for the trapezoidal rule and one for Simpson's rule \[ \int_{-1}^{1}\left(2 x^{2}+5\right) d x \] An upper bound for \( \left|E_{S}\right| \) is b. Evaluate the integral directly and find \( \left|E_{S}\right| \). \[ \int_{-1}^{1}\left(2 x^{2}+5\right) d x= \] (Type an exact answer. Type an integer or a simplified fraction.) \[ \left|E_{S}\right|= \] c. Use the formula \( \left\langle\left|E_{S}\right|\right. \) (true value)) \( \times 100 \) to express \( \left|E_{S}\right| \) as a percentage of the integral's true value. (Round to the nearest integer as needed.) II. Using Simpson's rule a. Estimate the integral with \( n=4 \) steps and find an upper bound for \( \left|E_{S}\right| \). \( S= \) (Type an exact answer. Type an integer or a simplified fraction.) An upper bound for \( \left|E_{S}\right| \) is b. Evaluate the integral directly and find \( \left|E_{S}\right| \) \[ \int_{-1}^{1}\left(2 x^{2}+5\right) d x= \] (Type an exact answer. Type an integer or a simplified fraction.) \[ \left|E_{S}\right|= \]


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