Use polar coordinates to describe the region as shown in the figure below:
A) $R = \{ ( r , \theta ) : - 4 \leq r \leq 4,0 \leq \theta \leq \pi \}$
B) $R = \{ ( r , \theta ) : 0 \leq r \leq 8,0 \leq \theta \leq \pi \}$
C) $R = \{ ( r , \theta ) : 0 \leq r \leq 5,0 \leq \theta \leq \pi \}$
D) $R = \{ ( r , \theta ) : 0 \leq r \leq 2,0 \leq \theta \leq \pi \}$
E) $R = \{ ( r , \theta ) : - 6 \leq r \leq 6,0 \leq \theta \leq \pi \}$

Question

Use polar coordinates to describe the region as shown in the figure below: 
A) $R = \{ ( r , \theta ) : - 4 \leq r \leq 4,0 \leq \theta \leq \pi \}$ 
B) $R = \{ ( r , \theta ) : 0 \leq r \leq 8,0 \leq \theta \leq \pi \}$ 
C) $R = \{ ( r , \theta ) : 0 \leq r \leq 5,0 \leq \theta \leq \pi \}$ 
D) $R = \{ ( r , \theta ) : 0 \leq r \leq 2,0 \leq \theta \leq \pi \}$ 
E) $R = \{ ( r , \theta ) : - 6 \leq r \leq 6,0 \leq \theta \leq \pi \}$

Quizplus · Accepted Answer

The radius of the region extends up to $r=2$ and covers the area inside the semicircle with radius $r=2$. Since the region is bounded by the $x$-axis, the angle $	heta$ ranges from $0$ to $\pi$. Thus, the polar coordinates that describe the region are $R = \{(r,	heta) : 0 \leq r \leq 2, 0 \leq 	heta \leq \pi\}$, which is choice $\boxed{	extbf{(D)}}$.

Use Polar Coordinates to Describe the Region as Shown in the Figure