Find the area under the curve given by the function f(x)=x^3+x^2-a on the interval [-2,1]

Question

anonymous · Answer

are under the curve is found by integrating f(x) and evaluating the integral over the region between x = -2  and x=1

(In other words, evaluate the integral of f(x) at x=1  and subtract the value of the integral of f(x) at x = -2)

anonymous · Answer

Just tried to reference the text, but I'm having trouble with integrals

anonymous · Answer

I'm not an expert, but on one like this, set it up like this:

$$ f(x)=x^3+x^2-a$$
$$\int\limits_{-2}^{1} f(x)dx = \int\limits_{-2}^{1}(x^3+x^2-a)dx$$

anonymous · Answer

when you integrate a term like x^3, you end up with a term (x^4)/4 

The way to see this is that if you differentiated (x^4)/4, you would get 4(x^3)/4 which simplifies to x^3.

So integrating is finding the term that would to allow you to differentiate to get back to the original term.

On relatively easy ones like this, a shortcut is to increase the exponent by 1 and then divide the new term by the value of the exponent.

anonymous · Answer

OK, I think I'm tracking...

anonymous · Answer

good... it takes me a bit to type all this :)  so it's great if you can pick up the concept from what I've said so far... 

Do you want to post what you get?  I will help check it :)

anonymous · Answer

@JakeV8 Nice explained :)

anonymous · Answer

** Nicely.

anonymous · Answer

yea, I will try... Thanks for all the help!

anonymous · Answer

It's going to take me a while to work through my references though...so please don't wait on my account though. Thanks for the steer in the right direction... :)