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 $y = \cos x , 0 \leq x \leq \frac { \pi } { 2 }$, about the $x$-axis.
A) 14.42
B) 2.29
C) 1.15
D) 7.21

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 $ S = \int_{a}^{b} 2\pi y \sqrt{1 + (y')^2} \, dx $. For $ y = \cos x $, $ y' = -\sin x $. Thus, the integral becomes $ \int_{0}^{\pi/2} 2\pi \cos x \sqrt{1 + \sin^2 x} \, dx $. Evaluating this integral using numerical methods gives approximately 7.21.

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

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