Use the trapezoidal rule and Simpson's rule to approximate the value of the definite integral. Compare your result with the exact value of the integral. (Give your answers correct to 4 decimal places.) 3∫43x3dx; n=6

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A: It can be solved using substitution of integration.

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A: Since we are given with the multiple number of question answered according to the guideline.

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A: Explanation of the answer is as follows

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Q: Use n= 4 to approximate the value of the integral by the following methods: (a) the trapezoidal…

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A: a) we apply indefinite integral later we apply the lower and uper limits

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Q: jocos" (r² –6+ +1) di 2 4

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Q: (a) Use the Midpoint Rule with n = 6 to approximate integral Sc dx 8 x-6 x+8 Write your answer exact…

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Numerical Integration

In a mathematical investigation, numerical integration comprises a wide group of calculations for computing the mathematical estimation of definite integral, and likewise, the term is moreover in some cases used to depict the numerical solution of differential equations. The most important aspect of this theory is error analysis.