Have you tried drawing a sketch of the region? Also, surely from the given information you can at least see the lower bound for each variable...
Find the volume of the solid in the first octant bounded by the coordinates planes, the plane x=3 and the parabolic cylinder z = 4-(y^2).
Can you please explain how to find limits of x and y in this question as I am not clear how to find them.
Help would be appreciated.
http://img196.imageshack.us/img196/6752/20130530162.jpg
here is what I sketched. I think the lower limit of x will be 0 and upper limit will be 3 but I don't know about y
Its to confusing for me I am having difficult time solving these questions.
here is what I sketched.
http://img818.imageshack.us/img818/2...0530211915.jpg
I have got a little bit now I think I have sketched it again.
http://img716.imageshack.us/img716/888/paraxa.jpg
the lower limit of y will be 0 but what about the upper limit?
Your graph is not very clear. I take it that parabola is supposed to be the cylinder " " but it is drawn in the wrong direction. It goes up to z= 4 , at y= 0 and crosses the y-axis, z= 0, at y= 2. And the cylindrical surface extends parallel to the x-axis.
It should be clear that x goes from 0 to 4, that for each x, y goes from 0 to 2, and that, for each x and y, z goes from 0 to .
Here's the full graph.
Graph from the side:
Graph tilted to the right:
same graph tilted to the left:
Here is cyan
is dark blue
is red
is gray
and is yellow.
You need to find the volume of the area that is enclosed with cyan, dark blue, red, gray and yellow parts of the graph which is in the first octant.