Consider the following integral: 0 COS X (4x - 9n)(x + 9) (a) Locate and characterize...
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Consider the following integral: 0 COS X (4x - 9n)(x + 9) (a) Locate and characterize all singularities of the integrand in the complex z plane. 1 = dx (b) Locate and characterize all singularities of the integrand when cos x is replaced by eix ejz (and x by the complex variable z), i.e. (42-97) (z+9) (c) Define the contours required to evaluate the given integral (4x9n)(x+9) dx. ejx (d) Evaluate the integral as given in part (c) by use of the residue theorem. Consider the following integral: 0 COS X (4x - 9n)(x + 9) (a) Locate and characterize all singularities of the integrand in the complex z plane. 1 = dx (b) Locate and characterize all singularities of the integrand when cos x is replaced by eix ejz (and x by the complex variable z), i.e. (42-97) (z+9) (c) Define the contours required to evaluate the given integral (4x9n)(x+9) dx. ejx (d) Evaluate the integral as given in part (c) by use of the residue theorem.
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a The integrand has singularities where the denominator is zero ie where either x90 or 4x90 The first equation has two roots in the complex plane xi3 ... View the full answer
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