14.03 Applications of integration
Interactive practice questions
In a closed habitat, the population of kangaroos $P\left(t\right)$P(t) is known to increase according to the function $P'\left(t\right)=\frac{t}{2}+9$P′(t)=t2+9, where $t$t is measured in months since counting began.
Determine the total change in the population of kangaroos in the first $4$4 months since counting began.
Solve for $T$T, the number of months it will take from when counting began for the population of kangaroos to increase by $88$88.
The population growth rate of fish is given by $p\left(x\right)$p(x), as shown in the graph below.
The total population growth of fish over $n$n years is given by $\int_0^np\left(x\right)dx$∫n0p(x)dx as shown in the table below.
An object is cooling and its rate of change of temperature, after $t$t minutes, is given by $T'=-10e^{-\frac{t}{5}}$T′=−10e−t5.
Calculate the average rate of change $f\left(x\right)$f(x) if $f'\left(x\right)=12\sin6x$f′(x)=12sin6x over the domain $\frac{\pi}{6}\le x\le\frac{\pi}{3}$π6≤x≤π3.