let A be closed-interval Subset of REAL ; :: thesis: for r being Real holds integral (r (#) sinh ),A = (r * (cosh . (upper_bound A))) - (r * (cosh . (lower_bound A)))
let r be Real; :: thesis: integral (r (#) sinh ),A = (r * (cosh . (upper_bound A))) - (r * (cosh . (lower_bound A)))
A1: [#] REAL is open Subset of REAL ;
( sinh | A is continuous & sinh | A is bounded ) by Lm9, Lm14, INTEGRA5:10;
hence integral (r (#) sinh ),A = (r * (cosh . (upper_bound A))) - (r * (cosh . (lower_bound A))) by A1, Lm9, Th31, Th68, INTEGRA5:11, SIN_COS2:35; :: thesis: verum