Find the area of the region that lies beneath the given curve. $$y = \sin x , 0 \leq x \leq \frac { \pi } { 3 }$$
A) $1.500$
B) $1.450$
C) $- 0.500$
D) $- 1.500$
E) $0.500$

Question

Quizplus · Accepted Answer

The area under the curve $y = \sin x$ from $x = 0$ to $x = \frac{\pi}{3}$ is found by integrating $\sin x$ over this interval: $\int_0^{\frac{\pi}{3}} \sin x \, dx = [-\cos x]_0^{\frac{\pi}{3}} = -\cos(\frac{\pi}{3}) + \cos(0) = -\frac{1}{2} + 1 = \frac{1}{2} = 0.500$.

Find the Area of the Region That Lies Beneath the Given