How do I solve for dP in this integral equation?

[s7b]

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?

 

[Fayez]

$$\int B dT = \int k \text{dP} \rightarrow BT + C_1 = kP + C_2$$
combine $$C= C_1 -C_2$$
$$\frac{BT + C}{k} = P$$

 

[s7b]

How are you supposed to solve something like that not knowing what C is though?

 

[Fayez]

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