The rumen is the first division of the stomach of a ruminant, or cud-chewing animal. An article on the rumen microbial system reports that the fraction of the soluble material passing from the rumen without being fermented during the first hour after its ingestion could be calculated by the integral

where k measures the rate that the material is fermented.

(a) Determine the integral, and evaluate it for the following values of k used in the article: 1/12, 1/24, and 1/48 hour.
(b) The fraction of intermediate material left in the rumen at 1 hour that escapes digestion by passage between 1 and 6 hours is given by

Determine this integral, and evaluate it for the values of k given in part (a).

Transcribed Image Text:

['ke (1 Jo ke-kt (1 t) dt,