Let R be the region bounded by y = 1/x, the lime x = 1, the line x = 3 and the x-axis. The line x = k divides R into two regions of equal area. Determine k.

Answer 1

so
[integral] 1/x dx form 1 to k = [integral] 1/x dx from k to 3
lnx from 1 to k = lnx from k to 3
ln k - ln1 = ln3 - lnk
2lnk = ln3 + ln1
ln (k^2) = ln3 + 0
k^2 = 3
k = √3

Answer 2

Thank you!!