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Integration Problems

Q#1)

dA
--- = -6t^9 - 6t^4 + 4
dt

A= ?

Q#2)

The rate of growth of the population, N(t), of a newly incorporated city t years after incorporation is estimated to be

dN
--- 1200sqrt(t) + 400, 0 < t < 16 (less than or equal to)
dt

If the population was 5000 at that time of incorporation, find the population 16 years later.

Solution Preview

Q#1)
dA
--- = -6t^9 - 6t^4 + 4
dt
A= ?

Multiply both sides by dt: dA = (-6t^9 - 6t^4 + 4)dt

Integrate both sides: A + c = (-6/10)t^10 - (6/5)t^5 + 4t + c

Simplify: A = (-3/5)t^10 - (6/5)t^5 + 4t + c

The answer is A = (-3/5)t^10 - (6/5)t^5 + 4t + c.

Q#2)
The rate of growth of the population, N(t), of ...

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