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NDA2015MathematicsDefinite IntegrationActual

_ -1 ^1 x | x | dx is equal to

Options

  1. A0
  2. B2/3
  3. C2
  4. D-1

Correct answer

A. 0

Step-by-step solution

aligned & _ -1 ^1 x|x| d x & = _ -1 ^0 x|x| d x+ ₀^1 x|x| d x & = _ -1 ^0 x(-x) d x+ ₀^1 x x d x & =- _ -1 ^0 x^2 d x+ ₀^1 x^2 d x & =- [ x^3 3 ]_ -1 ^0+ [ x^3 3 ]₀^1 & =- [0- (-1)^3 3 ]+ 1 3 [(1)^3-(0)^3 ] & =- 1 3 + 1 3 =0 aligned

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