(2a) The average of f(x) = cos(3x) (2b) The average of f(x) = x² (2c) The average of f(x) = 2x sin(x) (2d) The average of f(x) = 3x from 7/2 to T from (–10) to (10) from 0 to ↑ %3| from (-3) to (3)

Please use one of the following formulas: F=-k∆d   f=(1/2π)(√(k/m))    T=2π√(m/k)   f=(1/2π)(√(g/L))    T=2π√(L/g)   v=d/t   v=λf   fd=fs(v+vd)/(v-vs)   f=1/T   T=1/f   v=4Lf   v=2Lf   f=(1/2L)√(FT/μ)

(3) The natural independent variables for U are (S, V), from dU = TdS – pdV. U = U(S,V) (), instead. Show that U = U (V,T) leads to a much more complicated expression for p, namely gives simple expressions for T and p as T = and ().: Suppose you use (V,T) p = - V dT + f(V), %D T where f (V) is an unknown function of V.