Integrate the function (x-4)/(x^2+4) from 0 to 2

grouchy

I'm stuck on a calculus problem.

The intagral (from 0 to 2) of (x-4)/(x^2+4)

I figure you can split it as

x/(x^2+4) - 4/(x^2+4)

but I have no idea what to do after.

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yaychemistry

Re: Integral

that looks like the right step. I would suggest two different strategies for each term in the integral then. The first one looks like a u-substitution. The second looks like one of those gross inverse trig function anti-derivatives, see if you can look them up.

grouchy

Re: Integral

humm...I get

1/2ln(x^2 + 4) - 2arctan(x/2)

can someone double check for me? I'm pretty sure its right

Re: Integral

looks good to me

mbmcgee

Re: Integral

humm...I get

1/2ln(x^2 + 4) - 2arctan(x/2)

can someone double check for me? I'm pretty sure its right

I think it should be 1/2 ln(x^2 + 4) - arctan(x/2). Take a look at the second integral; when you factor out the 4 in the denominator it will cancel with the 4 in the numerator so it should not be -2arctan(x/2) but just -arctan(x/2).

Also don't forget your limits of integration

Dick

Homework Helper
Re: Integral

No, it's -2*arctan(x/2). grouchy's answer is correct. What's your problem? I think you are forgetting the dx part. Differentiate the given answer to check.

mbmcgee

Re: Integral

No, it's -2*arctan(x/2). grouchy's answer is correct. What's your problem? I think you are forgetting the dx part. Differentiate the given answer to check.
Ah. Oops. Your right.

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