Question #e3d0f

Question

1771 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-12-25T19:07:24

$9pi$

while you can use shell method, i think it's easier to rewrite y=x as a function of y and use disc method to rotate about the y-axis.

as a function of y, y=x becomes x=y.

using disc method, the volume of the solid is: $piint_a^b(r(y))^2dy$

a and b are the upper and lower bounds of integration. in this problem, $b=3$ and $a=0$ (because x=y intersects the axis of rotation at $(0,0)$ )

r(y) is the distance between the function and the axis of rotation. in this problem, $r(y)=y-0=y$

plugging in: volume= $piint_0^3y^2dy$
$=pi(F(3)-F(0))$ , where $F(y)=1/3y^3$ or the antiderivative of $y^2$ .

$=pi(1/3(3)^3-1/3(0)^3)$
$=pi(9-0)=9pi$