CPM Homework Help : APCALC Problem 12-83

Multiple Choice: Without a calculator, determine the area of the region in the second and third quadrants bounded by the polar curve $r ( \theta ) = \sqrt { \frac { 8 \theta } { \pi } }$ , as shown at right.

$4π$

$8π$

$\frac { 2 \pi } { 3 }(3^{3/2} – 1)$

$\frac { 13 \pi ^ { 3 } } { 24 }$

$\frac { 18 } { \pi }$

Spiral going counter clockwise, starting at the origin, going up & right, turning at the following approximate points, @ (1, comma 1), turning up & left, @ (negative 1, comma 1), turning down & left, @ (negative 3, comma negative 0.5), turning down & right, @ (0, comma negative 3.5), turning up & right, ending @ (4, comma 0).

Step:

$\int_{\pi/2}^{3\pi/2}\frac{1}{2}\cdot\frac{8\theta}{\pi}d\theta$