Calc - Find the average value of : f(x) = 7sinx + 6cosx on the interval [0, 11/3 pi]

Answer 1

Average value = (1 / (11π/3 - 0)) ∫_{(from 0 to 11π/3)} [7sinx + 6cosx]dx

= [3/(11π)] [-7cosx + 6sinx]_{(from 0 to 11π/3)} = [3/(11π)][-7cos(11π/3) + 6sin(11π/3) + 7cos0 - 6sin0] =

[3/(11π)][-7/2 - 3√3 + 7] = [3/(11π)][7/2 - 3√3]