The figure shows the curve $y=x^2.$ The area of the shaded part between x = 0 and x = 6 is A then find A/8.

 

The area can be divided into strips by drawing ordinates between x = 0 and x = 6 at a regular interval of dx. Consider the strip between the ordinates at x and x + dx. The height of this strip is $y=x^2.$ The area of this strip is $dA=ydx=x^{2}dx.$The total area of the shaded part is obtained by summing up these strip-areas with x varying from 0 to 6. Thus, 

$A=\underset{0}{\overset{6}{\int }}{x}^{2}dx={\left[\frac{x^3}{3}\right]}_0^6=\frac{216-0}{3}=72$