# Thread: proving integral is negative (help!)

1. ## proving integral is negative (help!)

I did the first part already, by letting
u = ax => dx = du/a, then just substituting in the values.
How do i explain why its negative?

2. Originally Posted by gomes

I did the first part already, by letting
u = ax => dx = du/a, then just substituting in the values.
How do i explain why its negative?
For x > 0, $\displaystyle e^x>1+x$. Take reciprocals to get $\displaystyle e^{-x}<(1+x)^{-1}$. So the integrand is always negative and hence so is the integral.

3. Originally Posted by Opalg
For x > 0, $\displaystyle e^x>1+x$. Take reciprocals to get $\displaystyle e^{-x}<(1+x)^{-1}$. So the integrand is always negative and hence so is the integral.
Thanks