Question

Use a definite integral to find the area of the region between the given curve and the x-axis on the interval $[0,b]$:
$y=3x^2$

Answer 1

A $={\int }_0^{b}ydx={\int }_0^b{3x^{2}dx=\left|\frac{3x^3}{3}\right|}_0^b=b^3$