Hi, could someone explain step by step how to answer these questions please:
Calculate the volume:
1) z^2 + x^2 =1 and x+y+z=3, y=0
2) (x^2)/9 +(y^2)/4 =1, z=xy in the 1st quadrant
Thanks
Hi, could someone explain step by step how to answer these questions please:
Calculate the volume:
1) z^2 + x^2 =1 and x+y+z=3, y=0
2) (x^2)/9 +(y^2)/4 =1, z=xy in the 1st quadrant
Thanks
Always draw a graph it helps you see the volume that you are trying to find.
The equation is a circluar cylindar of radius 1 centered on the y axis. It's bottom is the xz plane(y=0) and it is cut by the plane .
To find the volume I want to use cylindrical coordinates, but since the cylindar is tipped over lets use this change of coordinates.
Now we get the integral
You could have also set up a double integral using the same idea where y is your height function.
I hope this helps.
Good luck.
Once again draw a graph.
The equation
Is an equation of an elliptic cylindar centered on the z axis. We are trying to find the volume under the surface z=xy inside the cylindar and in quadrant one.
the projection of the cylindar into the xy plane is the ellipse
We can islolate y in this expression to get
In the first quadrant
Now the inegral is
Good luck.