2 Problem 1: Let f be a function. (a) What is the definition of an integral, e.g., what does it mean to say | f (x)dx I? %3D (b) Give an example of a function which is defined on [a, b], but is not integrable. Problem 2: For the following statements, answer true or false. If the statement is true, provi a short reason. If the statement is false, provide a counterexample (or explain why). (a) If f is integrable on [a, b] and F,G are two different anti-derivatives of f, then F(x) G(x) +c for all x E a, b and some constant c E R. (b) If | f(x) d = g(x) dx, then every upper sum for f is an upper sum for g. (c) If f, g are polynomials such that g(x)7 0 for all a E [a, b), then f/g is integrable on [a, (d) If f is continuous, y is differentiable, p' is integrable, and y(a) = p(b), then: %3D | f(p(x))'(x)dx = 0. True %3D

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear re…

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.