Find the volume of the solid obtained by rotating the region enclosed by the lines $y=x$, $y=4-x$, and $y=0$ about the x-axis.
I can use any method for this problem, and I began by graphing. Which lead to a triangle over the $x$-axis. I'm really lost on how to do this, any help would be appreciated!
as you see the intersection point of the lines is $(2,2)$ then volume is $$V= \pi\int\limits_{0}^2x^2dx+\pi\int\limits_{2}^4(4-x)^2dx$$ then you can conclude.