JEE Main202628 January 2026Morning ShiftMathematicsDefinite IntegrationActual

The value of _ r=1 ²⁰ ( | ( ₀^ r x| x| d x ) | ) is _ _ _ _

Correct answer

Step-by-step solution

Let I_r = ₀^ r x| x| , dx .....(1) Apply King Property = ₀^ r (r - x)| x| , dx .....(2) By (1) + (2) 2I_r = ₀^ r r| x| , dx I_r = r 2 ₀^ r | x| , dx I₁ = 1 2 ₀¹ | x| , dx = 1 2 ₀^ | t| , dt = 1 2 (2) I₂ = 2 2 ₀² | x| , dx = 2 2 ₀^ 2 | t| , dt = 2 2 (4) S = 1 2 2 + 2 2 4 + 3 2 6 + + 20 2 (2 20) = 1 + 2 + 3 + + 20 = 20 21 2 = 210

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