Help with a level integration question-by parts Watch
Got a bit stuck on this integration question, I think they’ve used by parts-which I’ve tried to do, and let u= ln x and dv/dx=k. I don’t understand why they have got the integral of k dx (next to second red tick) rather than integral of k •1/x dx (as du/dx would be 1/x)?
Hope this explanation made sense☺️
The rate of change of y with respect to x is proportional to ln x. Fine y when x=8
Can you see the working out/markscheme clear enough?
When you do IBP, and you integrate one of the parts, you keep that integrated part for the second integral. So you've got , because you integrate k to get kx. They've skipped out the intermediate step of cancelling out the x's.