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.
Communication is effective because it allows individuals to share ideas, thoughts, and information with others.
effective communication can lead to improved outcomes in various settings, including personal relationships, business environments, and educational settings. By communicating effectively, individuals can negotiate effectively, solve problems collaboratively, and work towards common goals.
it starts up serve and return practice/assessments.it helps find voice talking therapy also assessments through relaxed conversation.
miss
Every time someone flushes a toilet in the apartment building, the person begins to jumb back automatically after hearing the flush, before the water temperature changes. Identify the types of learning, if it is classical conditioning identify the NS, UCS, CS and CR. If it is operant conditioning, identify the type of consequence positive reinforcement, negative reinforcement or punishment
nature is an hereditary factor while nurture is an environmental factor which constitute an individual personality. so if an individual's parent has a deviant behavior and was also brought up in an deviant environment, observation of the behavior and the inborn trait we make the individual deviant.
Samuel
I am taking this course because I am hoping that I could somehow learn more about my chosen field of interest and due to the fact that being a PsyD really ignites my passion as an individual the more I hope to learn about developing and literally explore the complexity of my critical thinking skills
hello. autism is a umbrella term. autistic kids have different disorder overlapping. for example. a kid may show symptoms of ADHD and also learning disabilities.
before treatment please make sure the kid doesn't have physical disabilities like hearing..vision..speech problem. sometimes these
Jharna
continue..
sometimes due to these physical problems..the diagnosis may be misdiagnosed.
treatment for autism.
well it depends on the severity.
since autistic kids have problems in communicating and adopting to the environment.. it's best to expose the child in situations where the child
Jharna
child interact with other kids under doc supervision.
play therapy.
speech therapy.
Engaging in different activities that activate most parts of the brain.. like drawing..painting. matching color board game.
string and beads game.
the more you interact with the child the more effective
Jharna
results you'll get..
please consult a therapist to know what suits best on your child.
and last as a parent. I know sometimes it's overwhelming to guide a special kid.
but trust the process and be strong and patient as a parent.
Jharna
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