Use your grapher to find the surface's area numerically.
-$$y = \sin x , 0 \leq x \leq \pi / 4 ; x \text {-axis }$$
A) 5.46
B) 8.18
C) 2.42
D) 14.32

Question

Quizplus · Accepted Answer

The surface area of a curve $y = f(x)$ rotated around the x-axis from $x=a$ to $x=b$ is given by the formula $$S = 2\pi \int_{a}^{b} y \sqrt{1 + \left(\frac{dy}{dx}\right)^2} dx.$$ For $y = \sin x$, $dy/dx = \cos x$, so the formula becomes $$S = 2\pi \int_{0}^{\pi/4} \sin x \sqrt{1 + \cos^2 x} dx.$$ Numerically integrating this expression gives a value close to 2.42.

Use Your Grapher to Find the Surface's Area Numerically y=sin⁡x,0≤x≤π/4;x-axis y = \sin x , 0 \leq x \leq \pi / 4 ; x \text {-axis }y=sinx,0≤x≤π/4;x-axis

Use Your Grapher to Find the Surface's Area Numerically $y = \sin x , 0 \leq x \leq \pi / 4 ; x \text {-axis }$