How do I solve for dP in this integral equation?

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    Integrals
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Discussion Overview

The discussion revolves around solving an integral equation involving the variables P and T, specifically focusing on how to isolate dP. Participants explore different approaches to manipulating the equation and express confusion regarding the integration constants involved.

Discussion Character

  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • One participant expresses confusion about solving the equation BdT = KdP and arrives at B(T2-T1) = K(P2-P1), questioning the correctness of their result.
  • Another participant suggests integrating both sides of the equation, leading to the expression BT + C_1 = kP + C_2, and proposes combining the constants into a single constant C.
  • A participant questions how to determine the constant C without additional information.
  • Another participant proposes that P is a function of T, suggesting that knowing a specific value of P at T=0 can help solve for C, leading to a derived expression for P(T).

Areas of Agreement / Disagreement

Participants do not reach a consensus on how to handle the integration constant C, and there is uncertainty regarding the correctness of the initial manipulations of the equation.

Contextual Notes

Participants highlight the dependence on the integration constant C and the need for initial conditions to fully resolve the equation, indicating that the discussion is limited by these unresolved aspects.

s7b
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Its been a while since I took calculus so I'm confused as how to solve this.

I've gotten my equation simplified as far as

BdT=KdP and I'm supposed to solve for dP

I do it and end up with B(T2-T1) = K(P2-P1)
but this is giving me the wrong answer when I put the values in...

What am I doing wrong?
 
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\int B dT = \int k \text{dP} \rightarrow BT + C_1 = kP + C_2
combine C= C_1 -C_2
\frac{BT + C}{k} = P
 
How are you supposed to solve something like that not knowing what C is though?
 
P is a function of T
P(T)
suppose you have a value of P(0) then to solve for C
T=0
P(0) = \frac{C}{k}

therefore,
P(T) = \frac{B}{k} T + P(0) = \frac{B}{k} T + \frac{C}{k}
 

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