JEE Main20253 Apr 2025Evening ShiftMathematicsDefinite IntegrationActual

The integral ₀^ 8 x d x 4 ^2 x+ ^2 x is equal to

Options

A2 ^2
B4 ^2
C^2
D3 ^2 2

Correct answer

A. 2 ^2

Step-by-step solution

aligned & I= ₀^ 8 x d x 4 ^2 x+ ^2 x & I= ₀^ 8( -x) d x 4 ^2 x+ ^2 x aligned 2 I =8 ₀^ d x 4 ^2 x+ ^2 x 2 I =8 2 ₀^ / 2 ^2 x 4+ ^2 x dx aligned & I =8 ₀^ dt 4+ t ^2 =8 1 2 ( ⁻¹ t 2 ]₀^ & =4 2 =2 ^2 aligned option (1)

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