Can someone help me with this Calculus question? I don't know where to start:

Find the area between the graph of f(x) = (x2 – 4) (x2 - 1) and the x axis. Note that one simple definite integral won’t do it, you will need to carefully determine where the function is positive and negative and integrate accordingly, perhaps using multiple steps.

Question

Can someone help me with this Calculus question? I don't know where to start:

Find the area between the graph of f(x) = (x2 – 4) (x2 - 1) and the x axis. Note that one simple definite integral won’t do it, you will need to carefully determine where the function is positive and negative and integrate accordingly, perhaps using multiple steps.

anonymous · Answer

Also:
I am allowed to use the program "Wolfram Alpha" to answer this question, if that helps.

anonymous · Answer

so you want to find the area enclosed by the function and the x-axis?

anonymous · Answer

I think so. :)

anonymous · Answer

if that is the case, just find where the function crosses the x-axis.  this is done by setting f(x)=0=(2x-4)(x2-1) and solving for x, which should have two solutions.  I can see by the equation that if x was 2 (where 2*2-4=0) or 0.5 (0.5*2-1=0) then this is where the function crosses the axis

anonymous · Answer

then, all you have to do is integrate the function from the starting point to the end point.  You should get a negative answer, but that's because it's area below the x-axis.  Since you are only looking for total area, just take the absolute value of this number, ignoring the negative sign.

anonymous · Answer

Ah, okay! :) Thank you for the reply! It makes sense now.