Find the surface area or volume.
-The region between the curve $y = \sin x , 0 \leq x \leq 1.9$, and the $x$-axis is revolved about the $x$-axis to generate a solid. Use a table of integrals to find, to two decimal places, the volume of the solid generated.
A) 3.66
B) 3.47
C) 3.53
D) 3.31

Question

Quizplus · Accepted Answer

The volume of the solid generated by revolving the region between the curve $y = \sin x$ and the $x$-axis from $x = 0$ to $x = 1.9$ around the $x$-axis can be found using the formula for the volume of a solid of revolution, $V = \pi \int_{a}^{b} [f(x)]^2 dx$, where $f(x) = \sin x$, $a = 0$, and $b = 1.9$. Therefore, the volume is $V = \pi \int_{0}^{1.9} (\sin x)^2 dx$. Using a table of integrals or appropriate computational tools to evaluate this integral and then multiplying by $\pi$, we find the volume to be approximately 3.47.

Find the Surface Area or Volume y=sin⁡x,0≤x≤1.9y = \sin x , 0 \leq x \leq 1.9y=sinx,0≤x≤1.9

Find the Surface Area or Volume $y = \sin x , 0 \leq x \leq 1.9$