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JEE Main20258 Apr 2025Evening ShiftMathematicsDefinite IntegrationActual

The integral _ -1 ^ 3 2 ( | ^2 x ( x) | ) d x is equal to:

Options

  1. A3+2
  2. B4+
  3. C1+3
  4. D2+3

Correct answer

C. 1+3

Step-by-step solution

Let, I = ^2 _ -1 ^ 3 / 2 | x x | dx aligned & = ^2 _ -1 ^1 x xdx - ₁^ 3 / 2 x xdx & = ^2 2 ₀^1 x xdx - _ -1 ^ 3 / 2 x xdx aligned Consider aligned & x xdx & - x 1 x + 1 1 xdx & =- x x + x ^2 aligned aligned I & = ^2 2 (- x x + x ^2 )₀^1- (- x x + x ^2 )₁^ 3 / 2 & = ^2 2 - (- 1 ^2 - 1 ) & = ^2 3 + 1 ^2 & =3 +1 aligned

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