Solution:
To calculate the average distance between the given parabola and the x-axis
y = 77x(1616 - x)
x ∈ [0, 16]
avg distance = [tex]\int_{0}^{16}\frac{77x(1616 - x)dx}{\int_{0}^{16} x dx}[/tex]
= [tex]2\int_{0}^{16}(\frac{(124432x - 77x^{2})dx}{[x^{2}]_{0}^{16}}[/tex]
=[tex] 2\int_{0}^{16}\frac{\frac{124432x^{2}}{2}- \frac{77x^{3}}{3}}{[x^{2}]_{0}^{16}}[/tex]
= [tex]16^{2}[\frac{62216 - 25.67\times 16}{16^{2}}][/tex]
avg distance = 61805 unit
