Approximate the area under the curve $y = \sin x$ from 0 to $\frac { \pi } { 2 }$ using 8 approximating rectangles of equal widths and right endpoints. The choices are rounded to the nearest hundredth.
A) $3.09$
B) $1.09$
C) $4.09$
D) $0.09$
E) $2.09$

Question

Quizplus · Accepted Answer

The interval from 0 to $\frac{\pi}{2}$ is divided into 8 equal parts, each with a width of $\frac{\pi}{16}$. The right endpoints are $\frac{\pi}{16}, \frac{2\pi}{16}, \ldots, \frac{8\pi}{16}$. The sum of the areas of the rectangles is $\sum_{k=1}^{8} \sin\left(\frac{k\pi}{16}\right) \cdot \frac{\pi}{16}$, which approximates to 1.09 when calculated.

Approximate the Area Under the Curve y=sin⁡xy = \sin xy=sinx From 0 To

Approximate the Area Under the Curve $y = \sin x$ From 0 To