I'm stuck on 1biii. I know the integral is V= (triple integral signs) dxdyz but I'm not sure how to work out the limits
Stuck on volume integral Watch
- Thread Starter
Last edited by bobbricks; 18-05-2016 at 21:59.
- 18-05-2016 21:58
- Study Helper
- 18-05-2016 22:56
You have one limit fixed, 1 or 2.
The other comes from rearranging the equation of the plane into z=....
Can you take it from there?
- 18-05-2016 23:43
1. You should draw a diagram to get a feel for the volume to be traversed.
2. Draw a picture of the shadow on the x-y plane of the region in question. Then choose suitable limits for x and y. One of these must have constants as upper and lower limits. You should imagine a thin strip parallel to either the x or y axes, and which is dragged from some constant value of x or y to another, thus covering the whole of the required x-y region. If you choose the strip parallel to the y-axis, then the coords of the top and bottom of the strip will be functions of x.
3. Note that you want to "integrate out" a variable each time you evaluate one of the iterated integrals e.g. you want something like:
Here, when we integrate against z, we remove z, but leave a function of (x,y) for the y-integral; when we deal with the y-integral, we leave a function of x only for the x-integral, and the x-integral finally removes the x dependence as it has constant limits.