Question

Why are the following integrals divergent?

\[\int\limits_{1}^{\infty}(x+1)dx/(x^{2} +2x)\]

\[\int\limits_{2pi}^{\infty}\sin(x)dx\]

Answer 1

sin(x) is divergent because it does not have a limit, it will be between [-1,1] and the sum will never converge.

Answer 2

The other one I suspect it's because the antiderivative will be logs. When t -> infinity, the log will diverge and the integral will diverge.

Answer 3

x/(x+2) is divergent thus the entire integral is divergent

Answer 4

for the first one

Answer 5

This is what I mean: \[lim_{t \rightarrow \infty} \int_{1}^{t} \frac{x+1}{x^2 + 2x} dx = lim_{t \rightarrow \infty} (\ln{t} + \ln{t+2})\]Can be thought that way too.

Answer 6

Should be ln(t+2)

Answer 7

you can split it