# Thread: Integration Question

1. ## Integration Question

Hello,

I'm trying to work through this problem and seem to be misunderstanding it, because I'm getting the wrong answer...
"A company has about 20 billion barrels of oil in reserve. To find the number of uears that this amount will last solve the equation

$\displaystyle Definite Integral (T over 0) of 1.2e^{0.04t} = 20$

I thought that to solve this, I'd essentially have to determine the integral of the equation at the top, and then solve for t. So I had something like this.

Integral of above $\displaystyle = 30e^{0.04t} = 20$
$\displaystyle = e^{0.04t} = 2/3$
$\displaystyle = 0.04t = ln (2/3)$
$\displaystyle = t = \frac {ln (2/3)}{0.04}$
$\displaystyle = t = -10.1$

This isn't the answer I'm supposed to get, according to the back of the book, but I'm obviously misinterpreting what the question is asking here...

Can someone give me a tip as to what I'm supposed to do, so that I can complete the question properly?

Thanks

2. ## Re: Integration Question

you are solving for T , the upper limit of integration ... you need to use the Fundamental Theorem of Calculus

$\displaystyle \int_0^T 1.2e^{.04t} \, dt = 20$

$\displaystyle \left[30e^{.04t}\right]_0^T = 20$

$\displaystyle 30 \left[e^{.04T} - e^0 \right] = 20$

$\displaystyle e^{.04T} - 1 = \frac{2}{3}$

solve for T ...

3. ## Re: Integration Question

Ah, thankyou, it was that upper-case T that was throwing me off...I didn't quite know what to do with it, so I was getting a little confused on what to do with it.

Thanks again, won't have any problems with what you've given me