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

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

Si 3 x(x + 1)dx

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

dx 2(x + 6x)

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

x = a cost, y = b sint (0 t )

where a and b are positive coordinates. Let A, x̅ and Iy 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

1 = +a?A + axA

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