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Q : Let d/dx [f(x)] = esinx / x , x > 0 .

If ∫ (2 esinx^2 / x) dx = f(k) - f(1) where limits of integration is from 1 to 4 , then k = .........

asked in Engineering Mathematics by Veteran (87k points) 15 57 292 | 160 views

1 Answer

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Let x2 = t,     Limit value  x = [ 1 , 4 ]  => t = [ 1 , 16 ] 

 

And  2x dx = dt

=>  2dx / x = dt / x2 = dt /  t.

 

   ∫ (2 esinx^2 / x) dx

= ∫  (esin t ) / t dt 

= ∫ F ' ( t) dt                      // d/dx [f(x)] = esinx / x , x > 0

= [F(t) ]116

= F(16 ) - F(1) 

 

Ans - k= 16. 

answered by Veteran (27k points) 13 48 207

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