Definite Integration Questions with Solutions

A definite integral gives a number rather than a family of functions. It is evaluated using the fundamental theorem of calculus: the integral of f(x) from a to b equals F(b) - F(a), where F is an antiderivative of f. This topic covers evaluating definite integrals, substitution with a change of limits, integration by parts with limits, and the definite integral as the limit of a sum. The properties of definite integrals are the key to most exam questions. The most useful is the "a + b - x" (or "a - x") property, which turns many difficult integrals into simple ones by adding the integral to itself. Also remember that the integral of an odd function over a symmetric interval from -a to a is zero, while the integral of an even function equals twice the integral from 0 to a. Practise the definite integration questions below, each with a step-by-step solution showing which property is used.