Finding unknowns inside integration of exponential function

Question

I have this equation:

$$\int_1^N a \ e^{-bx} dx = k$$

, where $N, k$ are constants. Is it possible to find the values of $a$ and $b$ that satisfy the above equation?

Answer 1

I figured it out, all I have to do is to perform the definite integration:

$$\int_1^Nae^{-bx}dx = \frac{a(e^{-b}-e^{-bN})}{b}$$

and then set $b$ equals to 1 or any other constant

$$\frac{a(e^{-1}-e^{-N})}{b} = k$$

and solve for $a$

$$a = \frac{kb}{e^{-1}-e^{-N}}$$