Initial Problem:
https://www.wolframalpha.com/input/?i=limit+(integral+from+0+to+a+of+(xln(1-x)))+as+a->1-
After taking the integral without its borders, and solving it with integration by parts:
https://www.wolframalpha.com/input/?i=limit+(ln(1-a)(a^2-1))/2+-(a(1+a/2))/2+as+a->1-
Graph of the function inside the limit:
https://www.desmos.com/calculator/mbarwveofq
I don't know how to properly solve the limit. Maybe it's no biggie, but any help is appreciated.
https://www.wolframalpha.com/input/?i=limit+(integral+from+0+to+a+of+(xln(1-x)))+as+a->1-
After taking the integral without its borders, and solving it with integration by parts:
https://www.wolframalpha.com/input/?i=limit+(ln(1-a)(a^2-1))/2+-(a(1+a/2))/2+as+a->1-
Graph of the function inside the limit:
https://www.desmos.com/calculator/mbarwveofq
I don't know how to properly solve the limit. Maybe it's no biggie, but any help is appreciated.