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Simpson's Rule and Composite Simpson's Rule and Errors

(4.3) 4d Find a bound for the error using Simpson's rule and compare this to the actual error for the following integrals (4.4) 2b Use the composite Simpson's rule to approximate the following integrals. , n = 4 Please see the attached file for the fully formatted problems.

Complex Integration : Holomorphisms

Let f(z) be holomorphic on the unit disc and f(0)=1. By working with 1/2ipi(integral over unit circle of [2+,-(z+1/z)]f(z) dz/z) prove that a)2/pi(integral(0 -2pi) of f(e^itheta)cos^2theta/2 d(theta))=2 + f'(0) b)2/pi(integral(0-2pi) of f(e^itheta)sin^2theta/2 d(theta))=2-f'(0)

Contour Integrals

Prove that integral (0 to pi/2) of sin^2n theta d(theta)=pi(1x3x5x...2n-1)/2(2x4x6x...2n)

Evaluating Integrals

Integrate the definite integral: |t|*e^-|t| from -infinity to infinity Is this a divergent or convergent integral and if the latter what is the answer?


Integration 1. Given that express in terms of x. 2. Find using substitution u = 1-x2. Explain results geometrically. See attached file for full problem description.

Evaluating Definite Integrals

Two definite integrals to evaluate. See attached file for full problem description. keywords: integrals, integration, integrate, integrated, integrating, double, triple, multiple

Using Shell Method to Evaluate Integrals

Use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region about the x-axis: y=x^3, x=0, y=8

Find the definite integral

(See attached file for full problem description) Find the definite integral __ ∫-18 3√x dx Note - The 8 is supposed to be directly over the -1.

Evaluating Integrals

Find the value of the integral - 6 ∫ x dx 4 Note - The 6 is supposed to be directly over the 4.


Antidifferentiation ∫(e^x -6) dx