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Most Important Selected Qs for JEE AdvancedMathematicsDefinite Integration

If L= ₀^ n e^ -x ( ^4 a x+ ^2 a x ) d x ₀^ e^ -x ( ^4 a x+ ^2 a x ) d x , where a R then:

Options

  1. AIf a=1 , then _ n L < 1
  2. BIf a=2 , then _ n L>1
  3. CIf a=3 , then _ n L < 1
  4. DIf a=4 , then _ n L>1

Correct answer

D. If a=4 , then _ n L>1

Step-by-step solution

Let f(x)=e^ -x ( ^4 a x+ ^2 x ) ₀^ n f(x) d x= ₀^ f(x) d x+ _ ^ 2 f(x) d x _ x= +t + _ 2 ^ 3 f(x) d x _ x=2 +t + + _ (n-1) ^ n f(x) d x _ x=(n-1) +t array ll & = ₀^ f(x) d x (1+e^ - +e^ -2 + .+e^ -(n-1) ) for a I & L=1+e^ - +e^ -2 + .+e^ -(n-1) a I & _ n L= 1 1-e^ - >1 a I array

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