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A quadratic equation, or equation of degree 2, is a second-degree polynomial equation in one variable. The standard form is:

\[ax^2 + bx + c = 0 \quad a \neq 0\]

Integration by substitution is a technique used to simplify an integral by introducing a suitable substitution.

The method of integration by parts allows us to rewrite the integral of the product of two functions in a simpler form. It is given by the formula:

\[\int u \, dv = uv – \int v \, du\]

Area between two curves \( f(x) \) and \( g(x) \) over \([a, b]\) is given by the integral \( \int_a^b [f(x) – g(x)]\,dx \), assuming \( f(x) \geq g(x) \).

Improper integrals are integrals in which either the interval of integration is unbounded, or the integrand becomes unbounded at one or more points, or both.