Find the integral of modulus of x^3-x dx within the limits 2 and -1. Please Be fast.

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Please find below the solution to the asked query:

We know that:X=Xif X>0-Xif X0;iWe have:I=-12 x3-xdx=-11 x3-xdx+12 x3-xdxWe know that:-aa fxdx=20a fxdx if fx is an even function. f-x=fxAs fx=x3-x is an even function, hence we get:I=201 x3-xdx+12 x3-xdxNow x3-x=xx2-1=xx-1x+1By method of interval. we get:x3-x=xx-1x+1<0 when x0,1and x3-x=xx-1x+1>0 if x1Hence using i, we get:I=-201x3-xdx+12x3-xdx=-2x44-x2201+x44-x2212=-214-12-0+164-42-14-12=-2-14+2+14=12+2+14=114=2.75Hence -12 x3-xdx=2.75

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