Evaluate the definite integral of the odd function
over the interval
The graph is shown in
[link] . We can see the symmetry about the origin by the positive area above the
x -axis over
and the negative area below the
x -axis over
We have
The net change theorem states that when a quantity changes, the final value equals the initial value plus the integral of the rate of change. Net change can be a positive number, a negative number, or zero.
The area under an even function over a symmetric interval can be calculated by doubling the area over the positive
x -axis. For an odd function, the integral over a symmetric interval equals zero, because half the area is negative.
Key equations
Net Change Theorem
or
Use basic integration formulas to compute the following antiderivatives.
Write an integral that expresses the increase in the perimeter
of a square when its side length
s increases from 2 units to 4 units and evaluate the integral.
A regular
N -gon (an
N -sided polygon with sides that have equal length
s , such as a pentagon or hexagon) has perimeter
Ns . Write an integral that expresses the increase in perimeter of a regular
N -gon when the length of each side increases from 1 unit to 2 units and evaluate the integral.
The area of a regular pentagon with side length
is
pa2 with
The Pentagon in Washington, DC, has inner sides of length 360 ft and outer sides of length 920 ft. Write an integral to express the area of the roof of the Pentagon according to these dimensions and evaluate this area.
A dodecahedron is a Platonic solid with a surface that consists of 12 pentagons, each of equal area. By how much does the surface area of a dodecahedron increase as the side length of each pentagon doubles from 1 unit to 2 units?
With
p as in the previous exercise, each of the 12 pentagons increases in area from 2
p to 4
p units so the net increase in the area of the dodecahedron is 36
p units.
An icosahedron is a Platonic solid with a surface that consists of 20 equilateral triangles. By how much does the surface area of an icosahedron increase as the side length of each triangle doubles from
a unit to 2
a units?
Write an integral that quantifies the change in the area of the surface of a cube when its side length doubles from
s unit to 2
s units and evaluate the integral.
Write an integral that quantifies the increase in the volume of a cube when the side length doubles from
s unit to 2
s units and evaluate the integral.
Bacteria doesn't produce energy they are dependent upon their substrate in case of lack of nutrients they are able to make spores which helps them to sustain in harsh environments
_Adnan
But not all bacteria make spores, l mean Eukaryotic cells have Mitochondria which acts as powerhouse for them, since bacteria don't have it, what is the substitution for it?
Assimilatory nitrate reduction is a process that occurs in some microorganisms, such as bacteria and archaea, in which nitrate (NO3-) is reduced to nitrite (NO2-), and then further reduced to ammonia (NH3).
Elkana
This process is called assimilatory nitrate reduction because the nitrogen that is produced is incorporated in the cells of microorganisms where it can be used in the synthesis of amino acids and other nitrogen products
There are nothing like emergency disease but there are some common medical emergency which can occur simultaneously like Bleeding,heart attack,Breathing difficulties,severe pain heart stock.Hope you will get my point .Have a nice day ❣️
_Adnan
define infection ,prevention and control
Innocent
I think infection prevention and control is the avoidance of all things we do that gives out break of infections and promotion of health practices that promote life