Volume of the solid of revolution for $f(x)=\sin x$
Find the colume of the solid obtained by rotating the graph of the function $y=\sin x$ around $x$-axis between $x=0$ and $x=\pi$.
Answer
The volume is given by the following integral
\[V=\int_0^{\pi}\pi \sin ^2 x dx=\pi \int_0^{\pi}\frac{1-\cos 2x}{2}dx\]
\[=\pi \left( \frac{x}{2}-\frac{\sin 2x}{4} \right) \bigg |_{x=0}^{x=\pi}=\pi (\frac{\pi}{2}-0)\]
\[=\frac{\pi^2}{2}.\]
The answer is accepted.
Join Matchmaticians Affiliate Marketing
Program to earn up to 50% commission on every question your affiliated users ask or answer.
- answered
- 480 views
- $2.00
Related Questions
- Compound Interest question
- Optimization problem
- Integration
- Find the domain of the function $f(x)=\frac{\ln (1-\sqrt{x})}{x^2-1}$
- Find the average of $f(x)=\sin x$ on $[0, \pi]$.
- A function satifying $|f(x)-f(y)|\leq |x-y|^2$ must be constanct.
- Can we use the delta-ep def of a limit to find a limiting value?
- Find $\lim_{x\rightarrow \infty} \frac{1}{x^2}\sin x^2\tan x$
