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Most Important Selected Qs for JEE AdvancedMathematicsIndefinite Integration

Let I= (e^x-1 )( x- x)+x x ^2 x+ (e^x-1-x )^2 d x= ⁻¹(f(x))+C , where ' C ' is the constant of integration and _ x 0 f(x)=0 . If _ x 0 f(x) x = p q , where p, q N then find the least value of (p+q) .

Correct answer

3

Step-by-step solution

aligned & I= (e^x-1 )( x- x)+x x ^2 x (1+ ( e^x-1-x x )^2 ) d x & Put, e^x-1-x x =t ( x) (e^x-1 )- (e^x-1-x ) x ^2 x d x=d t & (e^x-1 )( x- x)+x x ^2 x d x=d t & I= d t 1+t^2 = ⁻¹ ( e^x-1-x x )+C & f(x)= e^x-1-x x & _ x 0 f(x) x = _ x 0 e^x-1-x x ( x x ) x = 1 2 p q & . (p+q) |_ least =3 aligned

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