Turn on thread page Beta
    • Thread Starter
    Offline

    14
    ReputationRep:
    My notes say this:

    "Sometimes the order of the integration will determine whether or not it is necessary to split the region of integration..."

    But goes into no more detail?

    In which situations would you not need to split the region in one order, but you would in the other?

    Thankyou.
    Offline

    18
    ReputationRep:
    Consider the region D defined by 1-x^2 <= y <= 2(1-x^2), -1<=x<=1. (This is basically a region enclosed by two parabolas and the x-axis).

    If you do \displaystyle \int_{x=-1}^1 \int_{y=1-x^2}^{2(1-x^2)} f(x,y) \,dy\,dx you can do it in one go.

    But if you integrate the other way around, there are two 'ranges' of x value for each value of y. (Specifically, \sqrt{1-y}\le x \le \sqrt{1-y/2} and -\sqrt{1-y/2}\le x \le -\sqrt{1-y}), so you'd need to split into two separate regions.
    • Thread Starter
    Offline

    14
    ReputationRep:
    (Original post by DFranklin)
    Consider the region D defined by 1-x^2 <= y <= 2(1-x^2), -1<=x<=1. (This is basically a region enclosed by two parabolas and the x-axis).

    If you do \displaystyle \int_{x=-1}^1 \int_{y=1-x^2}^{2(1-x^2)} f(x,y) \,dy\,dx you can do it in one go.

    But if you integrate the other way around, there are two 'ranges' of x value for each value of y. (Specifically, \sqrt{1-y}\le x \le \sqrt{1-y/2} and -\sqrt{1-y/2}\le x \le -\sqrt{1-y}), so you'd need to split into two separate regions.
    I see.

    So any situation where, if you change the order, and the limits of integration can subsequently have 1 value or another, then you must split into two regions and sum them?
    Offline

    18
    ReputationRep:
    Pretty much. If you draw a sketch, it should be pretty obvious what's going on - it's just a hassle to do sketches on TSR.
 
 
 
Reply
Submit reply
Turn on thread page Beta
Updated: November 12, 2008

2,269

students online now

800,000+

Exam discussions

Find your exam discussion here

Poll
Should predicted grades be removed from the uni application process
Useful resources

Make your revision easier

Maths

Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

Equations

How to use LaTex

Writing equations the easy way

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups

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

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