# Thread: Converging and Diverging Improper Integrals I could not get!!!

1. ## Converging and Diverging Improper Integrals I could not get!!!

All the questions are uploaded on a jpeg and attached as a jpeg. It is the only format within MathType that I was able to export and open.

2. Originally Posted by daciernoj
All the questions are uploaded on a jpeg and attached as a jpeg. It is the only format within MathType that I was able to export and open.
(1) these are a lot of questions. I hope you are not trying to get us to do your homework for you.

(2) You should be able to get the sentences to look better with MathType

(3) You can copy code from MathType here, change the $and$ tags to [tex] [tex] tags and LaTeX will take care of the rest.

(4) Can you integrate these?

(5) you need to find where the integrands are undefined, and replace that point in the interval with a limit.

example, for the first: it is obviously undefined for x = 3. so the integral becomes

$\lim_{N \to 3} \int_N^4 \frac 1{(x - 3)^{3/2}}~dx$

integrate normally with the limits N and 4 and then take the limit as $N \to 3$ of the result. this will tell you if it diverges or not. It converges only if the result of taking the limit is finite.

(we always replace $\infty$ with a limit)

can you continue?