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∫02​(3t3+5t)dt I. Using the trapezoidal rule complete the following. a. Estimate the integral with n=4 steps and find an upper bound for ∣ET​∣. ∫02​(3t3+5t)dt= (Simplify your answer.) The upper bound is (Simplify your answer.)
The instructions for the given integral have two parts, one for the trapezoidal rule and one for Simpson's rule. Complete the following parts. ∫02​(3t3+5t)dt b. Evaluate the integral directly and find ∣ET​∣. ∫02​(3t3+5t)dt= (Simplify your answer.) ∣ET​∣= (Simplify your answer.)
The instructions for the given integral have two parts, one for the trapezoidal rule and one for Simpson's rule. Complete the following parts. ∫02​(3t3+5t)dt c. Use the formula (∣ET​∣/ (true value ))×100 to express ∣ET​∣ as a percentage of the integral's true value. % (Simplify your answer. Round to the nearest integer as needed.) II. Using Simpson's rule complete the following. a. Estimate the integral with n=4 steps and find an upper bound for ∣ES​∣. S= (Simplify your answer.) The upper bound is (Simplify your answer.)
The instructions for the given integral have two parts, one for the trapezoidal rule and one for Simpson's rule. Complete the following parts. ∫02​(3t3+5t)dt b. Evaluate the integral directly and find ∣ES​∣. ∫02​(3t3+5t)dt= (Simplify your answer.) ∣ES​∣= (Simplify your answer.) c. Use the formula (∣ES​∣/( true value ))×100 to express ∣ES​∣ as a percentage of the integral's true value.