Therefore, your average test grade is approximately 80.33, which translates to a B− at most schools.
Suppose, however, that we have a function
that gives us the speed of an object at any time
t , and we want to find the object’s average speed. The function
takes on an infinite number of values, so we can’t use the process just described. Fortunately, we can use a definite integral to find the average value of a function such as this.
Let
be continuous over the interval
and let
be divided into
n subintervals of width
Choose a representative
in each subinterval and calculate
for
In other words, consider each
as a sampling of the function over each subinterval. The average value of the function may then be approximated as
which is basically the same expression used to calculate the average of discrete values.
But we know
so
and we get
Following through with the algebra, the numerator is a sum that is represented as
and we are dividing by a fraction. To divide by a fraction, invert the denominator and multiply. Thus, an approximate value for the average value of the function is given by
This is a Riemann sum. Then, to get the
exact average value, take the limit as
n goes to infinity. Thus, the average value of a function is given by
Definition
Let
be continuous over the interval
Then, the
average value of the function
(or
fave ) on
is given by
Finding the average value of a linear function
Find the average value of
over the interval
First, graph the function on the stated interval, as shown in
[link] .
The region is a trapezoid lying on its side, so we can use the area formula for a trapezoid
where
h represents height, and
a and
b represent the two parallel sides. Then,
The definite integral can be used to calculate net signed area, which is the area above the
x -axis less the area below the
x -axis. Net signed area can be positive, negative, or zero.
The component parts of the definite integral are the integrand, the variable of integration, and the limits of integration.
Continuous functions on a closed interval are integrable. Functions that are not continuous may still be integrable, depending on the nature of the discontinuities.
The properties of definite integrals can be used to evaluate integrals.
The area under the curve of many functions can be calculated using geometric formulas.
The average value of a function can be calculated using definite integrals.
the study of living organisms and their interactions with one another and their environment.
Wine
discuss the biological phenomenon and provide pieces of evidence to show that it was responsible for the formation of eukaryotic organelles in an essay form
advantage of electronic microscope is easily and clearly while disadvantage is dangerous because its electronic. advantage of light microscope is savely and naturally by sun while disadvantage is not easily,means its not sharp and not clear
Abdullahi
cell theory state that every organisms composed of one or more cell,cell is the basic unit of life
Abdullahi
is like gone fail us
DENG
cells is the basic structure and functions of all living things
A scanning electron microscope (SEM) is ideal for situations requiring high-resolution imaging of surfaces. It is commonly used in materials science, biology, and geology to examine the topography and composition of samples at a nanoscale level. SEM is particularly useful for studying fine details,