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.
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I am allowed to use the program "Wolfram Alpha" to answer this question, if that helps.
so you want to find the area enclosed by the function and the x-axis?
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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
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.
Ah, okay! :) Thank you for the reply! It makes sense now.