Integral S (-sin(t))* exp(cos^3(t)) dt

Thread starter ori
Start date Sep 14, 2004
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Integral

In summary, the purpose of the integral S (-sin(t))* exp(cos^3(t)) dt is to find the area under the curve of the given function. To solve this integral, one can use integration by parts, substitution, or trigonometric identities. The limits of integration will depend on the specific problem or context. This integral can be evaluated analytically, but it may be complex. Real-world applications of this integral include calculating work done by a force and finding average values in various fields such as physics, engineering, and economics.

Sep 14, 2004

ori

integral
S (-sin(t))* exp(cos^3(t)) dt
t from 0 to 2pi
how do i solve it?
10x

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Sep 14, 2004

Tide

Science Advisor

Homework Helper

Study the SIGNS of the functions very carefully over the full period! :-)

Sep 14, 2004

ori

I know that
S sin(t) dt
t from 0 to 2pi
is 0
but why also
S (-sin(t))* exp(cos^3(t)) dt
t from 0 to 2pi
?

1. What is the purpose of the integral S (-sin(t))* exp(cos^3(t)) dt?

The purpose of this integral is to find the area under the curve of the function (-sin(t))* exp(cos^3(t)). This can be useful in many applications, such as calculating work done by a force or finding the average value of a function.

2. How do you solve this integral?

To solve this integral, you can use integration by parts or substitution. It may also be helpful to use trigonometric identities to simplify the integrand.

3. What are the limits of integration for this integral?

The limits of integration for this integral depend on the specific problem or context in which it is being used. Generally, the limits will be given in the problem or can be determined based on the given function and the desired area to be calculated.

4. Can this integral be evaluated analytically?

Yes, this integral can be evaluated analytically using integration techniques such as those mentioned above. However, the resulting integral may be complex and difficult to calculate without the use of a computer or calculator.

5. What are some real-world applications of this integral?

This integral can be applied in various fields, such as physics, engineering, and economics. For example, it can be used to calculate the work done by a varying force over a given distance or to find the average value of a varying quantity over a certain time period.