Integration

Jackie

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Apr 16, 2006
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So I'm supposed to find a bunch of stuff for this function but I'm stuck on the first part. The problem is:
Traffic flow is defined as the rate at which cars pass through and intersection, measured in cars per minute. The traffic flow at a particular intersection is modeled by the function F defined by
F(t)=82 + sin (t/2) for 0 < t < 30 where F(t) is measured in cars per minute and t is measured in minutes

(a) To the nearest whole number, how many cars pass through the intersection over the 30 minute period.


Ok so, I know that I need to do the integration of the function from 0 to 30 but the 4sin(t/2) part is really confusing me. please help!!
 
INT 82 + 4sin(t/2) dt = INT 82 dt + INT 4sin(t/2) dt

for the 2nd integral term ...
let u = t/2
du = (1/2)dt
you remember integration by substitution, don't you?


btw ... got news for you ... this was a calculator problem on the AP exam.
 
Have you found the antiderivative? that would be a good place to start evaluating the integral
 
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