We used to get lot of such tricky stuff during the preparation of IIT-JEE here in India, and I'm telling you if you don't understand Area under curve is integral, you can't touch most of the questions. But I get your point, if you are interested in such questions, you should checkout IIT JEE mathematics question, you'll love them
I am from a rural region where IIT-JEE is not that popular, and I liked working these physics and maths problems initially.
Unfortunately the competition has become so intense you practically need coaching (which is expensive) and dedicate lot of time, at that point it becomes grunt work. There are many "tricks" and "shortcuts" taught in these coachings which doesn't exists in normal NCERT syllabus. Needless to say I didn't do very well.
