# Very simple question on "definite integrals"

• Aug 17th 2011, 02:48 AM
jerk21189
Very simple question on "definite integrals"
Attachment 22078
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!
• Aug 17th 2011, 02:56 AM
Prove It
Re: Very simple question on "definite integrals"
No, you need to perform the integration first.
• Aug 17th 2011, 03:25 AM
jerk21189
Re: Very simple question on "definite integrals"
How to integrate that exponential function? I thought it remains the same after integration
• Aug 17th 2011, 03:25 AM
Siron
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:
$\frac{1}{3\cdot \ln(5)}\int_{0}^{1} e^{t}dt= ...$
• Aug 17th 2011, 06:48 AM
TheChaz
Re: Very simple question on "definite integrals"
Quote:

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!