Find the volume of the given solid.Bounded by the coordinate planes and the plane: 5x + 3y + z = 15
I do not know where I am going wrong. I found the intercepts, used point slope and integrated. My solution - 369/2 - is incorrect. any help?
Find the volume of the given solid.Bounded by the coordinate planes and the plane: 5x + 3y + z = 15
I do not know where I am going wrong. I found the intercepts, used point slope and integrated. My solution - 369/2 - is incorrect. any help?
well let's take a look.
at $z=0$ this reduces to
$5x + 3y = 15$
$y = 5 - \dfrac 5 3 x$
and as we are also bounded by $y=0$ we note that this occurs at $x=3$
so we integrate
$\displaystyle \int_0^3 \int_0^{5-\frac 5 3 x}\int_0^{15-5x-3y}~dz~dy~dx = \dfrac{75}{2}$