Calculate Probability Machine Part Lifetime < 6: Integration Problem

[stevecallaway]

Homework Statement

the lifetime of a machine part has a continuous distribution on the interval(0,40) with probability density function f, where f(x) is proportional to (10 + x)^(-2) Calculate the probability that the lifetime of the machine part is less than 6.

Homework Equations

The Attempt at a Solution

My book says that since f(x) is proportional to (10 + x), f(x)=k(10+x)^(-2). My question is why we need to put the k in the equation? Is it merely because the question says that they're proportional and so we need to set up that integration to find by how much they're proportional?

 

[ideasrule]

Yes.