Als je de kromme
y2 = x4 + x5
wentelt rond de x-as,
ontstaat er links van de y-as een peervormig lichaam.
De inhoud ervan is
|
A. \(\boldsymbol{\frac {11\pi} {30} }\) |
|---|
| B. \(\boldsymbol{\frac {\pi} {15} }\) |
| C. \(\boldsymbol{\frac {\pi} {30} }\) |
| D. \(\boldsymbol{\frac {11\pi} {15} }\) |
| E. \(\boldsymbol{\;\pi }\) |
[ 6-7060 - op net sinds 30.11.14-()-28.7.2024 ]
Translation in E N G L I S H
Oplossing - Solution
Snijpunten met de x-as (nulwaarden) : x4 + x5 = 0 ⇔ x4(1 + x) = 0 ⇔ x = 0 ∨ x = − 1
\(\boldsymbol{\int_{-1}^{0}\pi y^2dx=\pi\int_{-1}^{0}\:(x^4+x^5)\,dx=\pi\left (\left [ \frac{x^5}{5} \right ]_{-1}^{0}+ \left[ \frac{x^6}{6} \right ]_{-1}^{0}\right)=\pi\left ( \frac{1}{5}- \frac{1}{6}\right )=\frac{\pi}{30} }\)
