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Most Important Selected Qs for JEE AdvancedMathematicsDefinite Integration

Let I ₁= ₀^1 e ^ x 1+ x dx and I ₂= ₀^1 x ^2 e ^ x ^3 (2- x ^3 ) dx . The I ₁ I ₂ e is equal to ______

Correct answer

3

Step-by-step solution

Let t = x ^3 in I ₂ We have I₂= 1 3 ₀^1 1 e^t(2-t) d t= 1 3 ₀^1 1 e^ 1-t (1+t) d t I ₂= 1 3 e ₀^1 e ^ t (1+ t ) dt = 1 3 e l ₁ I ₁ el ₂ =3

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