If anyone can help me with this, I'd really appreciate it. Thanks! Find the volume of the solid generated by revolving the region bounded by the lines and curves about the x-axis. 1. y = x^2 , y= 0 , x = 2 2. y = x , y = 1 , x = 0
Follow Math Help Forum on Facebook and Google+
1. $\displaystyle \pi \int\limits_0^2 {\left[ {(x^2 )^2 - 0^2 } \right]} {\rm }dx = \pi \int\limits_0^2 {x^4 dx = } \pi \left. {\left[ {\frac{1}{5}x^5 } \right]} \right|_0^2 = \frac{{32}}{5}\pi $
2.$\displaystyle \pi \int\limits_0^1 {\left[ {(1)^2 - x^2 } \right]} {\rm }dx = \pi \int\limits_0^1 {(1 - x^2 )dx = } \pi \left. {\left[ {x - \frac{1}{3}x^3 } \right]} \right|_0^1 = \frac{2}{3}\pi $
View Tag Cloud