The Basic Idea of Calculus

The video tutorial introduces calculus as a subject focused on approximation. It explains the concept of slope and how to approximate it using points on a curve. The tutorial then discusses calculating the area under a curve using rectangles and improving these approximations with trapezoids. Despite different methods, all approximations converge to the same result. The video concludes by hinting at potential pitfalls in approximation methods.

What is the difference between using rectangles and trapezoids for area approximation?

What concern does the speaker raise about approximations in calculus?