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}} ...

Mathematics of Computation, Vol. 28, No. 126 (Apr., 1974), pp. 613-615 (7 pages) A new integral representation is derived for the expression $J_0(z)J_0(Z) + Y_0(z ...

Now that function-theory is fairly well developed, it is much easier than it used to be to discuss in an orderly way the elementary problems of explicit integration. By showing how this can be done, ...

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 ...

In the article, we prove that the function x→ ( 1−x ) p K( x ) is logarithmically concave on (0, 1) if and only if p ≥ 7/32, the function x→K( x )/log( 1+4/ 1−x ) is convex on (0, 1) and the function ...