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Most Important Selected Qs for JEE AdvancedMathematicsDefinite Integration

The value of ₀^ 4 e^ x (x+ 4 ) (1- x) x d x can be expressed as (a+ b ) e^ c -e d , then find the value of (a+b+c+d) .

Correct answer

7

Step-by-step solution

I= 1 2 ₀^ 4 e^ x x+ x (1- x) x d x Dividing numerator and denominator by ^2 x , we have aligned I & = 1 2 ₀^ 4 e^ x x x+ x ( x- x) d x I & = 1 2 ₀^ 4 e^ x ( x x ( x- x) + x ( x- x) ) d x I & = 1 2 ₀^ 4 e^ x ( x x ( 1 ( x- x) )+ ( x( x- x) ( x- x)^2 ) ) d x f(x) & = 1 x- x I & = . 1 2 e^ x ( x- x) |₀ ^ 4 aligned Putting the limits, we have I= 1 2 ( e^ 2 2 -1 -e )= (1+ 2 ) e^ 2 -e 2 which gives, a=1 ; b=2 ; c=2 ; d=2 a+b+c+d=1+2+2+2=7

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