2. Integral calculus

Integrals and antiderivatives frequently appear in the problems engineers must solve. This is an area where symbolic computation can often be of great help. Indeed, deriving the expression for an antiderivative or a definite integral is generally a difficult task to perform analytically, due both to the complexity of the calculations and to the mathematical knowledge required.

Of course, the ultimate goal of integral calculus is very often numerical integration. A large number of high-performance numerical programs perform this operation. The usefulness of symbolic computation in this case stems from two factors. First, calculating the antiderivative of the expression to be integrated, when possible, often reduces errors caused by numerical integration methods and avoids instability issues. Second, if one needs to calculate, for example, an integral of the form:...