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Evaluate the integral $\int_0^1 x^2 dx$.

As $x$ approaches 0, $f(g(x))$ approaches 1. mathematical+analysis+zorich+solutions

Mathematical analysis is a branch of mathematics that deals with the study of limits, sequences, series, and calculus. This paper provides an overview of the key concepts and techniques in mathematical analysis, with a focus on solutions to selected problems. We draw on the textbook "Mathematical Analysis" by Vladimir Zorich as a primary reference. Evaluate the integral $\int_0^1 x^2 dx$