Let be a nonnegative function such that is continuous overthe interval Let be the
Chapter 15, Problem 58(choose chapter or problem)
Let f be a nonnegative function such that \(f^{\prime}\) is continuous over the interval [a, b]. Let S be the surface of revolution formed by revolving the graph of f, where \(a \leq x \leq b\), about the x-axis. Let x = u, y = f(u) cos v, and z = f(u) sin v, where \(a \leq u \leq b\) and \(0 \leq v \leq 2 \pi\). Then, S is represented parametrically by r(u, v) = ui + f(u) cos vj + f(u) sin vk. Show that the following formulas are equivalent.
Surface area = \(2 \pi \int_{a}^{b} f(x) \sqrt{1+\left[f^{\prime}(x)\right]^{2}} d x\)
Surface area = \(\int_{D} \int\left\|\mathbf{r}_{u} \times \mathbf{r}_{v}\right\| d A\)
Text Transcription:
f’
a <= x <= b
a <= u <= b
0 <= v <= 2 pi
2 pi int_a^b f(x) sqrt 1+[f’(x)]^2 dx
int_D int|r_u x r_v | dA
Unfortunately, we don't have that question answered yet. But you can get it answered in just 5 hours by Logging in or Becoming a subscriber.
Becoming a subscriber
Or look for another answer