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When I try to calculate the following integral in Mathematica 8, I get this strange result:
In[1]:= Integrate[y/((1 + x^2 + y^2)^(3/2)), {y, 0, 1}]
Maple 14 can solve this one easily:
Why is Mathematica giving me a different result?
707
The integration you are trying to compute will not give you any answer because the constant 'sigma v' has a subscript v which is considered as a variable v which runs from (-) Infinity to (+) Infinity. As Mathematica does not know that it is a subscript or a notation,it can not compute.
If your a is less than b, but your function over that interval is below the horizontal axis, then your definite integral is going to be negative.
Try this
r = Integrate[y/((1 + x^2 + y^2)^(3/2)), {y, 0, 1}]
r = Assuming[Element[x, Reals], Simplify[r]];
Together[r]
which gives
(-Sqrt[1+x^2]+Sqrt[2+x^2])/(Sqrt[1+x^2] Sqrt[2+x^2])
Which is the same as Maple's :
200
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