Note: This only works when \(x\) is measured in radians. We are now going to look at more complex trigonometric functions where we will use the general rule: \(\int {\cos (ax + b)dx = \frac{1}{a}} ...

Research in inequalities and integrals within the realm of fuzzy and interval-valued functions has advanced our understanding of uncertainty quantification and non-linear analysis. This field ...

Let $\gamma: \lbrack -1, 1 \rbrack \rightarrow R^n$ be an odd curve. Set $$H_\gamma f(x) = PV \int f(x - \gamma(t)) (dt/t)$$ and $$M_\gamma f(x) = \sup h^{-1} \int^h ...

A scheme of theorems is developed which enables an important class of integrals of the Schrodinger Hamiltonian between antisymmetric vector-coupled functions of the Russell-Saunders type to be ...