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Edexcel · Pure Maths · Integration
2:41
1
6 marks

Use integration by parts to find ∫ x ln x dx. Hence find the exact area between y = x ln x, the x-axis, and x = 1, x = e.

Worked Solution
M1Let u = ln x, dv = x dx → du = 1/x dx, v = x²/2
A1∫ x ln x dx = x²/2 · ln x − ∫ x/2 dx
A1= x²/2 · ln x − x²/4 + C
A1Area = [x²/2 · ln x − x²/4]₁ᵉ = (e²+1)/4
Your time: 2:41
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University of Oxford
University of Cambridge
Imperial College London
King's College London
London School of Economics
University of Warwick
University of Birmingham
Queen Mary University of London
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University of Warwick
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