Definate integral calculation difficulty

Hello,

The question is to evaluate the following integral.

by writing it as

I got

which I think is right, my difficulty seems to be with evaluating. The answer is given as , but I keep getting .

I'd be very grateful if someone would check this.

Thank you.

Re: Definate integral calculation difficulty

Hi Furyan!

You have a couple of singularities in there.

Perhaps you could split the integral in such a way you can take care of these singularities?

Re: Definate integral calculation difficulty

Quote:

Originally Posted by

**ILikeSerena** Hi Furyan!

You have a couple of singularities in there.

Perhaps you could split the integral in such a way you can take care of these singularities?

Hi ILikeSerena, I certainly feel very close to a black hole, but I'm afraid I can't resist the field strength(Crying). I figure since I've got the integral it should just be plain sailing. What do you mean by singularities?

Thank you

Re: Definate integral calculation difficulty

Re: Definate integral calculation difficulty

Re: Definate integral calculation difficulty

Quote:

Originally Posted by

**Furyan** Hi IlikeSerena,

Thank you for taking the time to post such a comprehensive reply. I now understand that the integral does not exist because you cannot integrate across a discontinuity. I also now see that it's important to sketch a graph when finding a definite integral and doing so helped me to see why I was getting a couple of other questions wrong.

Good!

Quote:

One thing that was confusing me was that when evaluating:

I got an error

but when evaluating

I got an answer of 0

The point is that you cannot divide by zero (or something bad happens to the universe, like black holes and singularities and stuff :D).

The tan function is actually a division of the sine by the cosine.

It does not exist if the cosine is zero, which is the case at 7pi/2, or more generally at pi/2 + k pi, where k is an integer.

When the tan does not exist, you can't take its inverse any more, even if that would have existed as in your case.

So does not exist, because it contains a division by zero.

But does exist, since there is no division by zero.

Quote:

I now have to evaluate:

Integrating I get

The given answer is

Am I right in thinking this integral does not exist either since

is not defined when

Thank you

Yes, you are correct. The integral does not converge due to the singularity at x=1.

Btw, your anti-derivative is not entirely correct, since it should also be defined for x < 1.

You lost that somewhere in your integration.

The anti-derivative you have only works for the part to the right of the singularity.

You would probably need to find another anti-derivative for the left part.

Re: Definate integral calculation difficulty

Quote:

Yes, you are correct. The integral does not converge due to the singularity at x=1.

Btw, your anti-derivative is not entirely correct, since it should also be defined for x < 1.

You lost that somewhere in your integration.

The anti-derivative you have only works for the part to the right of the singularity.

You would probably need to find another anti-derivative for the left part.

Thank you very much. Yes I can see that the anti-derivative only works for the part to the right of the singularity. For now I have no idea how I would go about finding another one for the left part, but I will think about it.

Thanks again for all your help.:)