Estimating Errors formulas in Theorem 4.20 to estimate the errors in approximating the integral, with n = 4, using (a) the Trapezoidal Rule and (b) Simpson's Rule. In Exercises 23-26, use the error %3D 23. 2x dx

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A: Given integral is,

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A: Please refer the attached image for complete solution.

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A: Here is the solution:

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A: We need to compute the given integral

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A: To evaluate ∫032sint-2tdt

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A: Let,

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A: Dear students, Since you have asked multiple questions in a single request, we will be answering…

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Q: 8 U 1.5 -1.5 e dx

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A: To evaluate: ∫  sec θsecθ+tanθ dθ

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A: Let, Then we integrate by substitution c=integrating constant

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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.