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5.2 5.3 Chase Clay ton Worksheet 12 Math 165 Fall 2017 1. Let uer) and v(x) be functions of z and consider the function u(x) | f(t) dt u(x) F(x) = where f is a continuous function (a) Find an expression forf FG) (b) Compute this expression if u(x) sinx,r(x)-x2 cos(re), and f(x)-vz2sinz 2 Assuming that f(x) dx = 2 and g(z) dz -4, evaluate/2f (x) 3g(a) dr. -30-4) 3. Assunne that / 3/(r) dz--2, / 5f(x) dr 7, and f(z)--1 and evaluate f(x) da and 3f (x) +2 dz. 4. Since f(x) S If(a) for all z show that f(x) dx If(x)ld 5. Assume that for b > 0 that f(x) dx = 1-b-1. Use this to calculate the following: (a) f(x) dz. (b) 3f(x) -4da. 6. Use geometric reasoning to justify the following "facts" (a) If /(z) is even then Lf(z)dz=rf(z)dz. (b) If f(r) is odd then ()dr o.