Problem

一、單選題

4. Which of the following integrals represents the area enclosed by the smaller loop of the graph of $r=1+2\sin\theta$?

(A) $\dfrac{1}{2}\int_{7\pi/6}^{11\pi/6}(1+2\sin\theta)^2\,\mathrm{d}\theta$

(B) $\dfrac{1}{2}\int_{7\pi/6}^{11\pi/6}(1+2\sin\theta)\,\mathrm{d}\theta$

(C) $\dfrac{1}{2}\int_{-\pi/6}^{7\pi/6}(1+2\sin\theta)^2\,\mathrm{d}\theta$

(D) $\int_{-\pi/6}^{7\pi/6}(1+2\sin\theta)^2\,\mathrm{d}\theta$

(E) $\int_{-\pi/6}^{7\pi/6}(1+2\sin\theta)\,\mathrm{d}\theta$。