How do you integrate xln(x) between the limits of 0 and 2?
In order to answer this question you need to use integration by parts.Using the standard integration by parts formula: ∫u dv/dx dx = uv-∫v du/dx dx.Let:u=ln(x) v=(1/2)x2du/dx=1/x dv/dx=xTherefore we get:I=[1/2xln(x)-1/2∫xdx]20We now know how to integrate x. It becomes 1/2x2. Therefore the overall integral becomes:I=[1/2xln(x)]20-[1/4x2]20I=2ln(2)-1I=ln(4/e)I ≈ 0.386
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