Question

The area bounded by the X-axis and the curve $y=4x(x-3)$

Answer 1

Given that:

$y=4x(x-3)$

When $y=0$, we get

$x=0,3$

Now, say the area bounded by X-axis and the curve is $A$ then

$A=|{\int }_0^3(4x^2-12x)dx|$

$A=|{\int }_0^{3}4x^{2}dx-{\int }_0^{3}12xdx|$

$A=|{\left[4\frac{x^3}{3}\right]}_0^3-{\left[12\frac{x^2}{2}\right]}_0^3|$

$A=|36-54|$

$A=18unit$

Hence, the area is $18units$.