Most Important Selected Qs for JEE AdvancedMathematicsDefinite Integration

Let I(n)= ₀^ (1-2 n x+n^2 ) d x . Find the value of I(100) I(10) .

Correct answer

Step-by-step solution

I(n)= ₀^ (1-2 n x+n^2 ) d x Using King and add I(n)= 1 2 ₀^ (1+n^4-2 n^2 2 x ) d x [Put 2 x=t] I(n)= 1 4 ₀^ 2 (t+n^4-2 n^2 t ) d t Using Queen aligned & I(n)= 1 2 ₀^ (1+n^4-2 n^2 t ) d t= 1 2 I (n^2 ) & I (n^2 ) I(n) =2 ; & Hence, I(100) I(10) =2 & aligned

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