Can someone help me with this problem

[Alif]

 

[Deleted member 4993]

View attachment 20433

Hint:

\(\displaystyle \frac{1}{(x-3)^2} \ = \ (x-3)^{-2}\)

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

https://www.freemathhelp.com/forum/threads/read-before-posting.109846/#post-486520​

Please share your work/thoughts about this assignment.

 

[HallsofIvy]

First, do you understand that, since the integrand is "undefined" at x= 3, this integral is really \(\displaystyle \lim_{a\to 3} \int_a^4 \frac{1}{(x- 3)^2}dx= \lim_{a\to 3}\int_a^4 (x- 3)^{-2}dx\)?

So, first, what is \(\displaystyle \int_a^4 (x- 3)^{-2}dx\)?