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#### rachelwind

##### New member

- Apr 13, 2013

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*So heres the question:*

If h(t) denotes the number of times a person’s heart beats in t minutes, then the pulse rate p beats per minute is given by p = dh/dt

During a workout an athlete has a pulse rate p(t) beats per minute where

p(t) = 58 + 10.62t^2(e^-0.25t)

t minutes after the start of the workout.

How many times does the athlete’s heart beat during the first 20 minutes of the workout? Give your answer to the nearest complete heartbeat.

If h(t) denotes the number of times a person’s heart beats in t minutes, then the pulse rate p beats per minute is given by p = dh/dt

During a workout an athlete has a pulse rate p(t) beats per minute where

p(t) = 58 + 10.62t^2(e^-0.25t)

t minutes after the start of the workout.

How many times does the athlete’s heart beat during the first 20 minutes of the workout? Give your answer to the nearest complete heartbeat.

Ive been told i need two applications of integration by parts. But i really dont know how to do this. Ive managed to do this so far:

Integral (58 dt) + 10.62 Integral ( t^2 e^(-t/4) dt )

58t + 10.62 Integral ( t^2 e^(-t/4) dt )

Let u = t^2. dv = e^(-t/4) dt.

du = 2t dt. v = (-4)e^(-t/4)

**Getting the answer:**

585 + (10.62)(-4)t^2 e^(-t/4) + (10.62)(8) Integral ( t e^(-t/4) dt )

Let u = t. dv = e^(-t/4) dt

du = dt. v = (-4)e^(-t/4)

**Then:**

585 + (10.62)(-4)t^2 e^(-t/4) + (10.62)(8)(-4)t e^(-t/4) - (10.62)(8)(-4) (-4)e^(-t/4) + C

Is this right so far? Or am i completely off track. Thanks