The area of the region (in sq.

Question

The area of the region (in sq. units), in the first quadrant, bounded by the parabola $y=9x^2$ and the lines $x=0$, $y=1$, $y=4$, is:

Accepted Answer

$x=\dfrac{\sqrt y}{3}$.

$$\text{Area} = \int_1^4\frac{\sqrt y}{3}\,dy = \frac13\left[\frac23y^{3/2}\right]_1^4 = \frac29\bigl(8-1\bigr) = \frac{14}{9}$$

Solutions · 1