Hey Pravar !
Your post indeed looks puzzling at first sight though its nomore a fallacy than saying both ±2 square to 4! Let me elaborate!
The integrity(literal, not mathematical) of the solutions can be checked by diffrentiating both to get the same result sinX.cosX so where lies the fault ?
Take the two solutions to integral (without the constants mind you... )
I1= (-1/4) * (cos2X)
I2 = (1/2) * (sin2X)
There you go pal with a little of simple maths ...
I1
= (-1/4)*cos2X
= (-1/4)*[1 – 2sin2X] =
= (-1/4) + (1/2)*(sin2X)
= constant + I2
So there ...
The two differ by just a constant!
No wonder they are integrals of the same expression!
It would be better (& correct) practice to insert the constants & then show the result but the catch remains the same...
BOTH THE RESULTS DIFFER BY A CONSTANT WHICH HAS NO EFFECT TO THE INTEGRATION !!!
~ TWISH ~
Well, I don't think we'll need any more explanations after that!!
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