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Improper integral. Not an improper integral. Find the area under the curve y = 7/cos2 t between t = 0 and t = 7T/2. If it converges, find the exact value. If it diverges, enter DIVERGES. The rate, r, at which people get sick during an epidemic of the flu can be approximated by r = 1200te 0-5f, where r is measured in people/day and t is measured in days since the start of the epidemic. When are people getting sick fastest? How many people get sick altogether? For a > 0, calculate the following. Use a lower case a.

Explanation / Answer

1) it is not a improper integral as the values of the function are never goint to infinity in the interval -8 to 0

2) the integral of the function is integral 7 sec^2x i.e 7 tanx from 0 to pi/2 i.e infinity => it diverges

3) a)third graph is the correct graph starts at 1200 and goes to 0 at infinity

b) people get sick faster at t=0 as r has highest value of 1200

c) integral r dt from 0 to infinity i.e. -1200/0.5 e^-0.5t from 0 to infinity so answer is 2400 people get sick

4) a) integral is -a/a e^(-y/a) from 0 to infinity i.e answer is 1

b) integral is -ye^(-y/a) - a e^(-y/a) from 0 to infinity i.e answer is a

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