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Question

Evaluate the following integrals:
14x-1+x-2+x-4 dx

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Solution

I=14x-1+x-2+x-4 dxI=14x-1 dx+14x-2 dx+14x-4 dxWe know that, x-1=-x-1 , x1x-1, 1<x4x-2=-x-2 , 1x2x-2, 2<x4x-4=-x-4 , 1x4x-4, x>4I=14x-1 dx-12x-2 dx+24x-2 dx-14x-4 dxI=x22-x14-x22-2x12+x22-2x24-x22-4x14I=8-4-12+1-2-4-12+2+8-8-2+4-8-16-12+4I=232

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