4.11. Let I(k)=eikt dt. (a) Show that I(0) = 1. (b) Show that I(k) = 0...

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4.11. Let I(k)=eikt dt. (a) Show that I(0) = 1. (b) Show that I(k) = 0 if k is a nonzero integer. (c) What is I()? 4.12. Compute fc021 z dz. CHAPTER 4. INTEGRATION 68 4.13. Show that z" dz = 0 for any closed piecewise smoothy and any integer n + -1. (If n is negative, assume that y does not pass through the origin, since otherwise the integral is not defined.) 4.11. Let I(k)=eikt dt. (a) Show that I(0) = 1. (b) Show that I(k) = 0 if k is a nonzero integer. (c) What is I()? 4.12. Compute fc021 z dz. CHAPTER 4. INTEGRATION 68 4.13. Show that z" dz = 0 for any closed piecewise smoothy and any integer n + -1. (If n is negative, assume that y does not pass through the origin, since otherwise the integral is not defined.)