Question

An area of algae, A(t), grows at a rate of A'(t) = sqrt(t)*ln(t) cm^2/day. How much additional
area does the algae aquire from day 1 to day 9?

Answer 1

so you need to find:\[\Large \int\limits_{0}^{9}\sqrt t \cdot \ln(t)dt\]

Answer 2

i think ingtegration by parts would work here

Answer 3

\[\int\limits u dv= uv -\int\limits v du\]

\[u= \ln(t) \dots du=\frac 1tdt\]\[dv= \sqrt tdt \dots v=\frac 23 t^\frac32\]

Answer 4

ok thanks man.

Answer 5

shouldn't it be from 1 to 9?

Answer 6

that part i am not sure of ....

i am reading the question to mean: from the beginning of the first day(t=0) to the end of the ninth day(t=9)


if it means: from the END of the first day to end of ninth day, then 1 to 9 is correct

Answer 7

ok thanks.