Check to see whether the integral can be evaluated easily by using another method. In some cases, it is more convenient to use an alternative method.
Substitute
and
This substitution yields
(Since
and
over this interval,
Simplify the expression.
Evaluate the integral using techniques from the section on trigonometric integrals.
Use the reference triangle from
[link] to rewrite the result in terms of
You may also need to use some trigonometric identities and the relationship
(
Note : The reference triangle is based on the assumption that
however, the trigonometric ratios produced from the reference triangle are the same as the ratios for which
A reference triangle can be constructed to express the trigonometric functions evaluated at
in terms of
Integrating an expression involving
Evaluate
and check the solution by differentiating.
Begin with the substitution
and
Since
draw the reference triangle in the following figure.
The domain of the expression
is
Thus, either
or
Hence,
or
Since these intervals correspond to the range of
on the set
it makes sense to use the substitution
or, equivalently,
where
or
The corresponding substitution for
is
The procedure for using this substitution is outlined in the following problem-solving strategy.
Questions & Answers
I'm interested in biological psychology and cognitive psychology
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