Apply the techniques of Example 7.1.5 to the evaluation of the improper integral 8 dx 1 = (a) Let oo+iy. (b) Let oo-iy. (c) Take the Cauchy principal value.

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Q: 1) Evaluate the integral 2) Evaluate the integral S 5 sec² t de (tant — - 1 dx 8 x√√x² 2

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A: To find out the integration.

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Q: Evaluate the improper intergal 1 dx using the residue (x² + 100)? theorem.

A: The given problem is to evaluate the given improper integral using the residue theorem. We have to…

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Q: 5. Solve, using the method of undetermined coefficients: y" + 2y' = 2x + 5 – e-2= %3D

A: First we shall get particular solution of y''+2y'=2x+5. Using method of undetermined coefficients y…

Q: 4. Use residue theory to calculate the following integrals: 3x (a) P.V. · Loo (2²+49) (2² - 2x + 5)²…

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Q: x8dx (а2+x?)2

A: We can solve this using substitution method and partial decomposition

Q: a) Let f(x) = 35 – 2a-1 +5+ 7x². Compute the integral of f. %3D

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A: The Fourier integral of a function f(x) is defined as:F(ω)=∫−∞∞f(x)e−iωxdxTo find the Fourier…

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