HELP AND I'LL WRITE YOU THE BEST TESTIMONY CHUCK NORRIS HAS EVER SEEN!

Find the area between the curves y = (x^2/2) +2 and –x-3 on the interval –4 ≤ x ≤ 4.

a) 40/3
b) 16
c)24
d)184/3
e)212/6

Question

HELP AND I'LL WRITE YOU THE BEST TESTIMONY CHUCK NORRIS HAS EVER SEEN!

Find the area between the curves y = (x^2/2) +2 and –x-3 on the interval  –4 ≤ x ≤ 4. 

a) 40/3 
b) 16
c)24
d)184/3
e)212/6

accessdenied · Answer

This sounds like a job for integration!

But first you might like to either graph this or figure out if either curve intersects each other on that interval.  We inevitably want to take the difference of the larger function and the smaller function so that it is always positive.

anonymous · Answer

Gotcha. Thanks. I'm not the best at integration.

anonymous · Answer

But I will try to graph it.

accessdenied · Answer

Once you can tell that one function is greater than the other, it is pretty much subtracting the smaller function from the greater and integrating over -4 to 4.  This one might be fine, but if they were to intersect, you would have to split the domain so that one function was greater than the other on one end, and then the opposite was true over the remaining domain.  This is because you want an overall area between these curves and if you start adding the "negative" areas it stops working.

mathstudent55 · Answer

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