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Most Important Selected Qs for JEE AdvancedMathematicsDefinite Integration

Let I₁= ₁^3 (x^2+x+3 ) f (x^3-2 x^2-5 x+2020 ) d x and I₂= ₁^3 (4 x^2-3 x-2 ) f (x^3-2 x^2-5 x+2020 ) d x . If the value of 2 I₁ 3 I₂ = a b where a and b are co-prime, then find the value of (a+b) .

Correct answer

5

Step-by-step solution

Consider I₂-I₁= ₁^3 (3 x^2-4 x-5 ) f (x^3-2 x^2-5 x+2020 ) d x Put aligned & Put & x^3-2 x^2-5 x+2020 & =t & & (3 x^2-4 x-5 ) d x & =d t & & I₂-I₁ & = ₂₀₁₄²⁰¹⁴ f(t) d t=0 aligned Hence, aligned I₂ & =I₁ 2 I₁ 3 I₂ & = 2 3 a b a+b=5 aligned

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