Practicing Success
The area under the curve $y=2 \sqrt{2 a x}$ bounded by the lines $x-4=0$, and $y=0$ is $(a>0)$ : |
$\frac{16 \sqrt{2 a}}{3}$ sq. units $\frac{8 \sqrt{2 a}}{3}$ sq. units $\frac{64 \sqrt{2 a}}{3}$ sq. units $\frac{32 \sqrt{2 a}}{3}$ sq. units |
$\frac{32 \sqrt{2 a}}{3}$ sq. units |
$y = 2\sqrt{2ax}$ x - 4 = 0 y = 0 for $x-4=0$ line $x=4$ at $x=4$ $y=2 \sqrt{2 a \times 4}=y=2 \sqrt{8 a}=4 \sqrt{2 a}$ finding area limit $\rightarrow x=0$ to $x=4$ Area = $\int\limits_0^4 2 \sqrt{2 a x} d x \Rightarrow 2 \sqrt{2 a} \int\limits_0^4 \sqrt{x} d x$ Area = $2 \sqrt{2 a}\left[\frac{x^{1 / 2+1}}{1 / 2+1}\right]_0^4$ $=\frac{2 \times 2 \sqrt{2 a}}{3}(4)^{3 / 2}$ $=\frac{8 \times 4 \sqrt{2 a}}{3}$ $=\frac{32 \sqrt{2 a}}{3}$ |