You are Here: Home >< Maths

# Stuck on volume integral Watch

1. 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
Attached Images

2. (Original post by bobbricks)
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
I'd make the inner integral wrt z.

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?
3. (Original post by bobbricks)
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
To add to the previous post:

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.

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: May 18, 2016
Today on TSR

### Am I pregnant?

...or just paranoid?

### A robot wrote Harry Potter?

Discussions on TSR

• Latest
• ## See more of what you like on The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

• Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams

## Groups associated with this forum:

View associated groups
Discussions on TSR

• Latest
• ## See more of what you like on The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

• The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.