Engineering Mathematics II Quiz

Reduction formula is an algebraic relation connecting two integrals, which allows for the simplification or transformation of an integral into a more manageable form for evaluation.

An example of a reduction formula for $\int \sin^n x dx$, where $n$ is a positive integer, is $I_n = \int \sin x dx = \int \sin^{n-1} x \cdot \sin x dx = -\sin^{n-1} x \cdot \cos x - \int (n-1) \sin^{n-2} x \cdot \cos^2 x dx$.

The purpose of Reduction Formulae is to simplify or transform integrals into more manageable forms, making them easier to evaluate.

Reduction Formulae are useful in simplifying complex integrals by providing a way to express them in terms of integrals that are either immediately integrable or easier to integrate.

Reduction Formulae are important in Engineering Mathematics as they provide methods for simplifying and evaluating integrals that arise in various engineering and applied sciences applications.