Thread: volume bounded by planes y = (x^2) , planes z = 0 , , z = 4 and y = 9

1. volume bounded by planes y = (x^2) , planes z = 0 , , z = 4 and y = 9

by using triple integral , find the volume bounded by planes y = (x^2) , planes z = 0 , , z = 4 and y = 9 .
My ans is 36 , but the ans is 144... Is my ans wrong ?

2. Re: volume bounded by planes y = (x^2) , planes z = 0 , , z = 4 and y = 9

Hey xl5899.

I think you may have the wrong region.

If you look at your diagram you have two regions [look at the xy plane for the moment and forget the z-plane].

You have two areas - one on each side of the line y = x^2.

Try drawing a diagram and do two sets of limits for each area [i.e. each side of that line] and verify that you are indeed integrating over the correct region of area.

If you aren't then the answer will be significantly different and I have a "hunch" you are integrating the wrong area.

The z-values won't matter because the function is [in this case] independent of the z-value and it should just be multiplied by the height [just like a cylinder is multiplied by the height after you get the area of the cross sectional circle].

3. Re: volume bounded by planes y = (x^2) , planes z = 0 , , z = 4 and y = 9

$\displaystyle y$ from $\displaystyle x^2$ to $\displaystyle 9$

4. Re: volume bounded by planes y = (x^2) , planes z = 0 , , z = 4 and y = 9

Originally Posted by Idea
$\displaystyle y$ from $\displaystyle x^2$ to $\displaystyle 9$
i get 72 now , still not 144

5. Re: volume bounded by planes y = (x^2) , planes z = 0 , , z = 4 and y = 9

x from -3 to 3