Rumen Fermentation 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
∫^1_0 ke^k2(1-t)dt,
where k measures the rate that the material is fermented. Source: Annual Review of Ecology and Systematics.
a. Determine the above 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 ∫^6_1 ke^-k2(6-t)/5 dt.
Determine this integral, and evaluate it for the values of k given in part a.
∫^1_0 ke^k2(1-t)dt,
where k measures the rate that the material is fermented. Source: Annual Review of Ecology and Systematics.
a. Determine the above 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 ∫^6_1 ke^-k2(6-t)/5 dt.
Determine this integral, and evaluate it for the values of k given in part a.
1 answer:
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