Question:

$\displaystyle\int_{\frac{3\sqrt{2}}{4}}^{\frac{3\sqrt{3}}{4}}\dfrac{48}{\sqrt{9-4x^2}}\,dx$ is equal to:

π/3

π/2

π/6

2π

Step-by-Step Solution

Key Concept: $\int\frac{48}{\sqrt{9-4x^2}}dx=\int\frac{48}{3\sqrt{1-(2x/3)^2}}dx=24\sin^{-1}\!\left(\frac{2x}{3}\right)+C$.

$2\pi$.

Correct Answer: 4