Turn on thread page Beta

What am I doing wrong with my integration? watch

    • Thread Starter

    " The temperature T(t) degrees Celsius in a room which is being heated by an electric fire approximately enjoys the equation:

    dT/dt = 4 - T/5

    where the second term on the right-hand side arises because of heat loss. Given that the temperature is 10 degrees Celsius at time t=0, find the temperature T(t) at time t and the final temperature of the room."

    What I did was separate 4 - T/5 into (1/5)(20-T) and then I am trying to integrate dT/(20-T) = dt/5.

    I integrated the LHS to get ln(20-T) and I thought the integral of the right hand side would simply be t/5 , but the answers keep saying its negative. It might just be me being stupid but where is this negative coming from? I got the whole equation correct except for this negative, and so I also keep getting the final answer wrong.

    My equation is T = 20 - 10e^(0.2t) but for the last bit, when t tends to infinity, I get the final temperature to be negative infinity. But if the 0.2t was negative, I would get the final temperature to be 20, which seems right. I just can't see where this negative 0.2 is coming from.

    Ask Nick Clegg!

    When you differentiate 20-T, the answer is -1. This means that when you do the substitution u=20-T for the integration, you have to replace dT with -du, so a minus sign must be somewhere in your answer.
Submit reply
Turn on thread page Beta
Updated: March 17, 2011
Cats or dogs?
Useful resources

Make your revision easier


Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here


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