For that first question, the standard trapezium rule works and you dont have to think about it being negative when x=1/2. Is this just a coincidence give that this is a log graph or does the trapezium rule formula always give the correct estimate no matter if the graph goes +ve/-ve?
I don't know what the 'standard trapezium rule' is. I assume it just has to do with using a negative length if the graph is below the x axis? If so, then yes that would always work
@@rtwodrew2 its the one thats like h/2(y0+2y1+...2yn-1+yn). I guess all that equation is doing anyway is summing up multiple trapeziums and traingles in the first place. I just plugged the corresponding values without thinking about subtracting that little triangle and it worked. Thanks for the info
Yeah so since it's using y values and not lengths any negative area will be automatically accounted for as you'll be using a negative side length to compute it. Never seen that formula before, although I see now that it is in the pearson textbook, I've always just completely ignored it it seems
