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Most Important Selected Qs for JEE AdvancedMathematicsDefinite Integration

If r₁, r₂ and r₃ are three values of r which satisfy the equation ₀^ / 2 ( x+r x)^3 d x- 4 r -2 ₀^ / 2 x x d x=2 then the value of 4 7 (r₁^2+r₂^2+r₃^2 ) is equal to

Correct answer

3

Step-by-step solution

aligned & I ₁= ₀^ / 2 ( x+ r x)^3 d x= ₀^ / 2 ^3 x+ r ^3 ^3 x +3 r ^2 x x +3 r ^2 x ^2 xdx & = 2 3 + 2 r ^3 3 + r ^2+ r & I ₂= ₀^ / 2 x xdx =( x x + x )₀^ / 2 = -2 2 & I = I ₁+ 4 r -2 I ₂=2 & 2 r ^3+3 r ^2-3 r +2=6 & 2 r ^3+3 r ^2-3 r -4=0 & r ₁=- 3 2 , r ₁ r ₂=- 3 2 , r ₁^2= 21 4 aligned

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