I was doing an integration question earlier on and I came across something that I would like to be cleared up. The question basically boiled down to:

[tex]

- \left[ {\cot \left( \theta \right) + \theta } \right]_{\frac{\pi }{6}}^{\frac{\pi }{2}} = - \left[ {\frac{{\cos \left( \theta \right)}}{{\sin \left( \theta \right)}} + \theta } \right]_{\frac{\pi }{6}}^{\frac{\pi }{2}}

[/tex]

Now if I just substitute the relevant values into the antiderivative it works out fine. However if I write the following I end up getting a 'weird' (I do not

know the right words to describe it ) answer(something involving 1/infinity).

[tex]

- \left[ {\cot \left( \theta \right) + \theta } \right]_{\frac{\pi }{6}}^{\frac{\pi }{2}} = - \left[ {\frac{1}{{\tan \left( \theta \right)}} + \theta } \right]_{\frac{\pi }{6}}^{\frac{\pi }{2}}

[/tex]

Can someone explain to me why this occurs? I can understand that when certain values are substituted in, 'weird' numbers appear but I cannot understand why the question works/does not work, depending on which way an expression is written(I am referring to the cotangent function), even though it is just the same thing. Any help would be good. I hope I was not unclear.

[tex]

- \left[ {\cot \left( \theta \right) + \theta } \right]_{\frac{\pi }{6}}^{\frac{\pi }{2}} = - \left[ {\frac{{\cos \left( \theta \right)}}{{\sin \left( \theta \right)}} + \theta } \right]_{\frac{\pi }{6}}^{\frac{\pi }{2}}

[/tex]

Now if I just substitute the relevant values into the antiderivative it works out fine. However if I write the following I end up getting a 'weird' (I do not

know the right words to describe it ) answer(something involving 1/infinity).

[tex]

- \left[ {\cot \left( \theta \right) + \theta } \right]_{\frac{\pi }{6}}^{\frac{\pi }{2}} = - \left[ {\frac{1}{{\tan \left( \theta \right)}} + \theta } \right]_{\frac{\pi }{6}}^{\frac{\pi }{2}}

[/tex]

Can someone explain to me why this occurs? I can understand that when certain values are substituted in, 'weird' numbers appear but I cannot understand why the question works/does not work, depending on which way an expression is written(I am referring to the cotangent function), even though it is just the same thing. Any help would be good. I hope I was not unclear.

Last edited: