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AP EAMCET20225 Jul 2022Evening ShiftMathematicsDefinite IntegrationActual

_ -1 ^1 x-x^2 3-|x| d x=

Options

  1. A7+18 3 / 2
  2. B18 9 / 4
  3. C7+9 9 / 4
  4. D7-18 3 / 2

Correct answer

A. 7+18 3 / 2

Step-by-step solution

aligned & _ -1 ^1 x-x^2 3-|x| d x & = _ -1 ^1 x 3-|x| d x- _ -1 ^1 x^2 3-|x| & =0-2 ₀^1 x^2 3-|x| d x [ x 3-|x| is odd and . & x^2 3-|x| is even ] aligned aligned & =-2 ₀^1 x^2 d x 3-|x| =2 ₀^1 x^2 x-3 d x & =2 ₀^1 (x+3+ 9 x-3 ) d x & =2 [ x^2 2 +3 x+9 |x-3| ]₀^1 & = [7+18 2 3 ] aligned

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