Thread: Some reassurance

Hello,

I would be most grateful if someone could check my work.

$\displaystyle
f(x)= (x-3)(e^\frac{-x}{4}-1)
$

Find the area enclosed by the graph of this function and the x axis between x=0 and x=6.

As the graph crosses the x-axis at x=0 and x=3 all values of x are positive between x=0 and x=3 all values of x>3 are negative.

It is necessary to to find the positive area bounded by x=0 and x=3 and subtract it from the negative area bounded by x=3 and x=6.

So


$\displaystyle
\int^{3}_{0}(x-3)(e^\frac{-x}{4}-1)dx -\int^{6}_{3}(x-3)(e^\frac{-x}{4}-1)dx
$

After hopefully performing the integration correctly I get an answer of 4.1319

Everything checks out to me, including your final answer.

Also, if you're allowed to do these problems on the calculator I would suggest using the absolute value button. It's for you to note that total area means positive and negative area, not just the integral, but if you need a quick calculation, I know on the TI models you can enter $\displaystyle \int |f(x)|dx$

Thanks for for that Jameson

Originally Posted by Jameson

Also, if you're allowed to do these problems on the calculator I would suggest using the absolute value button. It's for you to note that total area means positive and negative area, not just the integral, but if you need a quick calculation, I know on the TI models you can enter $\displaystyle |\int f(x)dx|$

No, Jameson it is.
$\displaystyle \int_a^b|f(x)|dx$