>>12938997Fucking tired of clueless highschoolers like you. The integral IS the area under a curve, whether you're talking about the Riemann integral or the Lebesgue integral. The equivalence between this area and the antiderivative is the fundamental theorem of calculus.
If you don't understand this basic fact then how the fuck can you understand the Riemann and Lebesgue integrals? The whole theory behind the integral starts with the need to calculate the are under a curve, first by approximating it by calculating the area of simple shapes and then taking the limit as the shapes get closer and closer to the curve. If you don't get this basic idea, what the fuck are you doing?
>>12938977> Is it true figures would have distracted from actual understanding of mathematical analysis?No. Pictures always help, especially for highly geometric subjects like analysis. All the best mathematics educators use pictures and diagrams, from Milnor to Serre.
As a rule of thumb, if you see two books on the same subject, one has pictures and the other doesn't, you should pick the one with pictures every time.
>>12939250>>12939323This.
>>12939726>Pages are expensiveNot in our time.
>>12939470>>12939733>>12939747You retards are sabotaging your own mathematics education just because you believe in dumb spooks like thinking that being able to read worse books makes you smarter. It doesn't, you're just wasting your time and making yourself like math less in the process (unless you're so retarded you actually don't care how interesting and well-presented the material is, as long as it makes you look smart to be able to repeat).
You will never make it in academia.
