Area bounded by y=4 and 4/(1+x^2)

The question asks for the area bounded by y=4 and 4/(1+x^2) from x=-1 to x=1.

I used definition integral to do this question and get (4x - 4*arctan(x)) from x=-1 to x=1.

However, when I plug in the numbers, I don't know which value to use for arctan(-1). If I use arctan(-1) = 3 pi/4, I would get an answer from the answer key. (The answer key says arctan(-1) = -pi/4.

How do I know which value I should use?

Please help me! Thanks!

Re: Area bounded by y=4 and 4/(1+x^2)

Hey LLLLLL.

You should use the principal branch which means answers lie in the range [-pi/2,pi/2] if you include -infinity and +infinity.

Re: Area bounded by y=4 and 4/(1+x^2)

Quote:

Originally Posted by

**chiro** Hey LLLLLL.

You should use the principal branch which means answers lie in the range [-pi/2,pi/2] if you include -infinity and +infinity.

Oh my! I totally forgot to check the thread!

Thank you so much for helping me!!