Definite integral of the rate of change of a quantity over an interval interpreted as the change of the quantity over the interval

Practice Questions

AP Calculus AB › Definite integral of the rate of change of a quantity over an interval interpreted as the change of the quantity over the interval

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If f(1) = 12, f' is continuous, and the integral from 1 to 4 of f'(x)dx = 16, what is the value of f(4)?

A pot of water begins at a temperature of $20^\circ C$ and is heated at a rate of $\tfrac{10}{(t+1)^2}$ degrees Celsius per minute. What will the temperature of the water be after 4 minutes?

If $y-6x-x^{2}=4$ ,

then at , what is 's instantaneous rate of change?

If a particle's movement is represented by $p=3t^{2}-t+16$ , then when is the velocity equal to zero?

$\begin{align*}&\text{The velocity of a particle is given as:}\&v(t)=\frac{(26sin(t + 2))}{3}\&\text{Find its change in position over the time interval }t=4,5.5\end{align*}$

A particle's movement is represented by $p=-t^{2}+12t+2$

At what time is the velocity at it's greatest?

$\begin{align*}&\text{The flow of water into a tank is given as:}\&\frac{dV(t)}{dt}=\frac{(57cos(3t))}{8}\&\text{Find the change in volume over the time interval }t=[1,6]\end{align*}$

$\begin{align*}&\text{The velocity of a particle is given as:}\&v(t)=\frac{(12e^{(t)})}{37}\&\text{Find its change in position over the time interval }t=[0.5,3]\end{align*}$

What is the domain of $f(x)=\frac{x+5}{\sqrt{x^2-9}}$ ?

$\begin{align*}&\text{The rate of change of the length of an elastic is:}\&\frac{dl(t)}{dt}=\frac{(73sin(t + 1))}{11}\&\text{Determine the change in length over the time interval }t=[3,5]\end{align*}$

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