Calculus: Early Transcendentals, Chapter 6, 6.5, Section 6.5, Problem 4

Find average value of t/sqrt(3+t^2)
over [1,3]
1/(3-1) int_1^3 t/sqrt(3+t^2) dt
We will solve this integral using u substitution.
Let u = 3+t^2
du = 2t dt
(du) / 2 = t dt
Substitute the u and du into the equation.
1/(3-1) int (1/2)(du)/sqrt(u)
1/4 *2sqrt(u)
1/2 sqrt(3+t^2)
evaluate the limits 3 and 1
1/2 (sqrt(12) - sqrt(4))
1/2 (sqrt(12) - 2)