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Find the total area of the region between the curve and the x axis. Y=x^3-4x -2<_x<_2

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I dont think my teacher wants us to integrate it! is there an alternate way?
You can use a summation of areas of rectangles under the graph. |dw:1354592872973:dw| Width of each rectangle will be: \[w={{b-a}\over n}\]Where b=right limit=2 a=left limit=-2 n=number of rectangles. Then: \[\sum_{n=1}^{n} w f(a+wn)\] But because the graph goes into the negative you'll need to find the area of -2<=x<=0 and add on the area of 0<=x<=2 to get the total area.
alright ill give it a shot thanks!

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