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# What am I doing wrong with my integration? watch

1. " 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.
3. When you differentiate , the answer is -1. This means that when you do the substitution for the integration, you have to replace with , so a minus sign must be somewhere in your answer.

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Updated: March 17, 2011
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