Given the functions f(x)=4x-x^2 and g(x)=x^2 -6x+8. Find the Area of the Region

Question

anonymous · Answer

Integral of top function- bottom function
Then you integrate from the points of intersection.

anonymous · Answer

ive done that but i dont think its working out, do you mind showing me?

anonymous · Answer

So what is the intersection of the two functions?

anonymous · Answer

wait, how do i know which function is on top and which is on the bottom

anonymous · Answer

If you graph them you can usually tell. That's the way that I usually do it.

Or you can find the intersection of both
Then you pick one in between. Solve for x for this number.  The one high is the above.

solomonzelman · Answer

yes, that is correct,   $\large\color{slate}{\displaystyle\int\limits_{1}^{4}f(x)-g(x)~dx}$

solomonzelman · Answer

here is the picture https://www.desmos.com/calculator/jqgahuskl6

solomonzelman · Answer

if you have any questions, ask.

solomonzelman · Answer

it is just a polynomial, shouldn't be an issue integrating it