Homework Estimate the following definite integrals using the Trapezoidal rule and Simpson's rule. Estimate the integral with n = 4 steps and find an upper bound for E, and Esl 3. ds

Q: eSz sin(6x)dx —

A: For the  I=∫eaxsin(bx) dx =eaxa2+b2asin(bx)-bcos(bx)+C (Using integration by parts)

Q: dx from a = 0 to b = 1 et + e-

A: Integrals in some cases can be simplified to standard integrals with relevant substitution. For…

Q: Use a change of variables or Table toevaluate the following definite integrals.

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Q: 3.S dx C. ez? D. ex А. х В.-х? cos x 4. S9 dx V1+sin x A. V1+sinx B. cosx C. sinx D. 1+ sinx

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Q: Evaluate the following integral. x² dx 2 1₁x²0x (225+x²)²

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Q: (s) [₂ x sin(x² - 1) cos(x² − 1) + 1 dæ -1

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Q: -1 tanx 4. 1+x?

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Q: → (+,-) (- -) J (4)

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Q: Use Table to evaluate the following definite integrals.

A: Given: ∫0110xdx

Q: W) Find the definite integral.

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Q: 4. f sin3x sin2xdx =

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Q: 0 1 2x (4 – x²) dx

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Q: X (sinx)dx xp(xu!s) )c) 35in (ux) 2020 +1 13.

A: For (1),   ∫33xπsinxdxNote that ∫aafxdx=0, a≠∞. So, =0

Q: use geometric rules to solve the following integral

A: The given integral: ∫13-2x+8dxWe have use geometric rules to evaluate the integral.

Q: Evaluate the integral, if possible. (Hint: use the table of integrals and substitution)

A: Use the properties of indefinite integral to simplify.Let w = x^4.Calculate dw and simplify using…