# Math Help - Very simple question on "definite integrals"

1. ## Very simple question on "definite integrals"

At this stage, can I simple plug in 1 and 0 into the exponential to get the answer?
By doing so, I would get 4/3. But the model answer is 4/[3xln(5)].
Thanks!

2. ## Re: Very simple question on "definite integrals"

No, you need to perform the integration first.

3. ## Re: Very simple question on "definite integrals"

How to integrate that exponential function? I thought it remains the same after integration

4. ## Re: Very simple question on "definite integrals"

You can use a small substitution if you want, let $y\cdot \ln(5)=t \Rightarrow dy=\frac{dt}{\ln(5)}$ therefore:
$\frac{1}{3\cdot \ln(5)}\int_{0}^{1} e^{t}dt= ...$

5. ## Re: Very simple question on "definite integrals"

Originally Posted by Siron
You can use a small substitution if you want, let $y\cdot \ln(5)=t \Rightarrow dy=\frac{dt}{\ln(5)}$ therefore:
$\frac{1}{3\cdot \ln(5)}\int_{0}^{1} e^{t}dt= ...$
This agrees with the result that you would get by first rewriting the integrand as $e^{\ln(5^y)} = 5^y$, then integrating. Of course, the "rule" for integrating $a^x$ for a > 0 comes from writing it in base e!