Mathematics, 12.02.2020 03:16 aangellexith4237
Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line.
y = ln 3x, y = 4, y = 5, x = 0; about the y-axis
The answer I got was (pi/18)(e^16-e^8) and that is wrong.
Answers: 3
![V = \int\limits^5_4 {\pi \left(\frac{e^y}{3}\right)^2} \, dy\\V = \frac{\pi}{9}\int\limits^5_4 {e^{2y}} \, dy\\\\V = \frac{\pi}{9}\left[\frac{e^{2y}}{2}\right]^5_4\\V = \frac{\pi}{9}(e^{10}/2 - e^8/2) = \frac{\pi}{18}(e^{10} - e^8)\\ V = \frac{\pi}{18}19045.5 \approx 3324](/tpl/images/0507/9419/3b844.png)
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