Question

trying to figure out if this integral converges or diverges. Integral from 0 to 29 of (7/(x^2-25))dx

Answer 1

the function is discontinuous at \(x=5\)
\[\large \int_0^{29}\frac{7}{x^2-25} dx=\lim_{A\rightarrow 5-}\int _0 ^A \frac{7}{x^2-25} dx +\lim_{B\rightarrow 5+}\int _B ^{29} \frac{7}{x^2-25} dx \]

Answer 2

that part I got but I can't figure out if it converges or diverges and if so where?

Answer 3

I believe to test for convergence you would just need to take the limit of f(x) as x goes to infinity. If it exists as a real number it converges, otherwise it diverges.

Answer 4

seems unlikely, because the anti derivative will be obtained by partial fractions i think, and you will get the log

Answer 5

the terms will involve \(\ln(x-5)\) and \(\ln(x+5)\) and as \(x\to 5\) \(\ln(x-5)\) goes to minus infinity

Answer 6

because each of the integral is divergent as suggested by @satellite73 , the original integral is divergent

Answer 7

oh right, I'm mixing this up with testing for convergence of sequences. Satellite73 is correct.

Answer 8

awesome, i got it now. thanks everyone!!!