(a) Using the substitution u = x + 1, evaluate

(b) Using the substitution u = √x + 6, evaluate

(c) The region R is bounded by the x axis, the line x = 9/2 and the curve with parametric equations

where a and b are positive coordinates. Let A, x̅ and I_y denote respectively the area of R, the x coordinate of the centroid of R and the second moment of area of R about the y axis. Prove that

Si 3 x(x + 1)dx