Find the surface area or volume.
-Use numerical integration with a programmable calculator or a CAS to find, to two decimal places, the area of the surface generated by revolving the curve $y = \sin 2 x , 0 \leq x \leq \frac { \pi } { 2 }$, about the $x$-axis.
A) 9.29
B) 14.42
C) 7.21
D) 1.48

Question

Quizplus · Accepted Answer

The surface area $S$ of a curve $y = f(x)$ revolved around the x-axis from $x = a$ to $x = b$ is given by the formula $S = 2\pi \int_{a}^{b} y \sqrt{1 + (\frac{dy}{dx})^2} dx$. For $y = \sin 2x$, $\frac{dy}{dx} = 2\cos 2x$. Substituting $a = 0$, $b = \frac{\pi}{2}$, and $y = \sin 2x$ into the formula and integrating using a CAS or programmable calculator gives a surface area of approximately 9.29 square units.

Find the Surface Area or Volume y=sin⁡2x,0≤x≤π2y = \sin 2 x , 0 \leq x \leq \frac { \pi } { 2 }y=sin2x,0≤x≤2π​

Find the Surface Area or Volume $y = \sin 2 x , 0 \leq x \leq \frac { \pi } { 2 }$