Answer
a) 2 ; b) $\dfrac{2a}{3}$
Work Step by Step
a. The average value is defined as:$\dfrac{1}{3} \int_{0}^3 \sqrt {3x} dx$
$\dfrac{\sqrt 3}{3} [\dfrac{x^{\frac{1}{2}+1}}{\frac{1}{2}+1}]_{0}^3=\dfrac{2\sqrt 3}{9} [3^{\frac{3}{2}}-0]=2$
b. The average value is defined as: $\dfrac{1}{a} \int_{0}^a \sqrt {ax} dx$
$\dfrac{\sqrt a}{a} [\dfrac{x^{\frac{1}{2}+1}}{\frac{1}{2}+1}]_{0}^a=\dfrac{2\sqrt a}{3a} [3^{\frac{a}{2}}-0]=\dfrac{2a}{3}$
