Reduction Formulae of 2-refined Neutrosophic Integrals and their Applications

The main aim of this manuscript is to establish for the first time the reduction formulae of 2-refined neutrosophic indefinite integrals (shortly, RF2RNII) which have double indeterminacy I1 and I2 respectably. We then verify reduction formulae with appropriate examples and also apply reduction formulae to evaluate definite integrals in 2-refined neutrosophic environment. The reduction formula of 2-refined trigonometric functions in 2-refined neutrosophic integrals (shortly, RF2RNI) is a useful mathematical technique for calculating and deriving a simplified version of integrals. We also classify these reduction formulae by investigating various cases of 2-refined neutrosophic integrals (shortly,2RNI).