JEE Main20245 Apr 2024Morning ShiftMathematicsDefinite IntegrationActual

The value of _ - ^ 2 y(1+ y) 1+ ^2 y d y is :

Options

A2 ^2
B^2 2
C2
D^2

Correct answer

D. ^2

Step-by-step solution

_ - ^ 2 y(1+ y) 1+ ^2 y d y (= (Odd) _ - ^ 2 y 1+ ^2 y d y + (Even) _ - ^ 2 y y 1+ ^2 y d y ) =0+2.2 ₀^ y ( y 1+ ^2 y ) d y aligned & I=4 ₀^ y y 1+ ^2 y d y & I=4 ₀^ ( -y) y 1+ ^2 y d y & 2 I=4 ₀^ y 1+ ^2 y d y & I=2 ₀^ y 1+ ^2 y d y & =2 (- ⁻¹( y) )₀^ & =-2 [ (- 4 )- ( 4 ) ] & =-2 [- 2 4 ]= ^2 aligned

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