Question

What is `f(x) = int e^(5x-1)+x dx` if `f(0) = -4`?

Answer 1

I tried this:

Explanation:

Given:
`f(x)=int(e^(5x-1)+x)dx`
let us solve the integral:
`f(x)=int(e^(5x-1))dx+intxdx`
`f(x)=(e^(5x-1))/5+x^2/2+c`
so now we need to evaluate the value of the constant `c`. We know that at `x=0` we have: `f(0)=-4` so using our function:
`f(0)=-4=(e^(5*color(red)(0)-1))/5+color(red)(0)^2/2+c`
`-4=e^-1/5+c`
so that:
`c=-e^-1/5-4`
and our function finally becomes:
`f(x)=(e^(5x-1))/5+x^2/2-e^-1/5-4`