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Evaluate the integral. ∫ 1 4 (6t3/2 i + (t + 8)tk)dt

Evaluate the integral. ∫ 1 4 (6t3/2 i + (t + 8)tk)dt

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Evaluate the integral.
∫ 1 4 ( 6 t 3 / 2 i + ( t + 8 ) t k ) d t

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The instructions for the given integral have two parts, one for the trapezoidal rule and one for Simpson's rule. Complete the following parts. ∫ 1 -1 (3x^2 + 7)dx. Using the trapezoidal rule a. Estimate the integral with n = 4 steps and find an upper bound for |ET|. T = (Type an exact answer. Type an integer or a simplified fraction.) An upper bound for |ET| is (Round to two decimal places as needed.) b. Evaluate the integral directly and find |ET|. ∫-1 1 (3x^2 + 7)dx = (Type an exact answer. Type an integer or a simplified fraction.) |ET| = (Round to two decimal places as needed.) c. Use the formula (|ET|/( true value )) × 100 to express |ET | 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 |ES|. S = (Type an exact answer. Type an integer or a simplified fraction.) An upper bound for |ES| is b. Evaluate the integral directly and find |ES |. ∫-1 1 (3x^2 + 7)dx = (Type an exact answer. Type an integer or a simplified fraction.) |ES| = c. Use the formula (|ES |/( true value) ) × 100 to express |ES| as a percentage of the integral's true value. % (Round to the nearest integer as needed.)

The instructions for the given integral have two parts, one for the trapezoidal rule and one for Simpson's rule. Complete the following parts. ∫ 1 -1 (3x^2 + 7)dx. Using the trapezoidal rule a. Estimate the integral with n = 4 steps and find an upper bound for |ET|. T = (Type an exact answer. Type an integer or a simplified fraction.) An upper bound for |ET| is (Round to two decimal places as needed.) b. Evaluate the integral directly and find |ET|. ∫-1 1 (3x^2 + 7)dx = (Type an exact answer. Type an integer or a simplified fraction.) |ET| = (Round to two decimal places as needed.) c. Use the formula (|ET|/( true value )) × 100 to express |ET | 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 |ES|. S = (Type an exact answer. Type an integer or a simplified fraction.) An upper bound for |ES| is b. Evaluate the integral directly and find |ES |. ∫-1 1 (3x^2 + 7)dx = (Type an exact answer. Type an integer or a simplified fraction.) |ES| = c. Use the formula (|ES |/( true value) ) × 100 to express |ES| as a percentage of the integral's true value. % (Round to the nearest integer as needed.)
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