Another Integration Question :S

  • Thread starter Redoctober
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    Integration
In summary, the conversation is about a student struggling with finding the integral of (sin(x-2))^(1/3). They attempted to use the substitution method and separate the function, but both methods did not work. Another person suggests trying a power series method, but the student is not familiar with it yet. The conversation ends with a suggestion to post the question in the Calculus and Beyond section.
  • #1
Redoctober
48
1

Homework Statement



∫(sin(x-2))^(1/3)

The Attempt at a Solution



I reached until -∫1/((1-u^2)^1/3).du where u = sin(x)
Then i got stuck as i tried to integrate to inverse function but it doesn't work as that is for ∫1/((a-x^2)^1/2)

another try was to separate the sin(x-2)

where i reached until

∫(1-(cos(x-2))^2)*(sin(x-2))^(5/3).dx
then using u= cos(x-2) u get -du=sin(x-2) . but this doesn't work too -.- !

Help
 
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  • #2
Do you know this or no?

NumberedEquation3.gif
 
  • #3
mtayab1994 said:
Do you know this or no?

View attachment 42204

Yes , this is the function of integration .
If u mean ∫(sin(x-2))^(1/3).dx = 3/4*cos(x-2)^(4/3) + C . it is wrong :S
 
  • #4
Redoctober said:

Homework Statement



∫(sin(x-2))^(1/3)

The Attempt at a Solution



I reached until -∫1/((1-u^2)^1/3).du where u = sin(x)
Then i got stuck as i tried to integrate to inverse function but it doesn't work as that is for ∫1/((a-x^2)^1/2)

another try was to separate the sin(x-2)

where i reached until

∫(1-(cos(x-2))^2)*(sin(x-2))^(5/3).dx
then using u= cos(x-2) u get -du=sin(x-2) . but this doesn't work too -.- !

Help
Hello Redoctober.

WolframAlpha leads me to believe that this can't be expressed in terms of elementary functions.

You might try a power series method.

By The Way: You should be posting these integration questions in the Calculus and Beyond section.
 
  • #5
SammyS said:
Hello Redoctober.

WolframAlpha leads me to believe that this can't be expressed in terms of elementary functions.

You might try a power series method.

By The Way: You should be posting these integration questions in the Calculus and Beyond section.

Oh k thanks :) . I think i ll keep it for later , as we didn't start yet with the power series method yet in the Calculus 1 course .

K i ll post in the Calculus and Beyond :) .
 

1. What is integration?

Integration is a mathematical concept that involves finding the area under a curve in a given interval. It is used in calculus to solve problems related to motion, area, and volume.

2. Why is integration important?

Integration is important because it allows us to solve problems that involve continuously changing quantities. It has numerous applications in fields such as physics, engineering, economics, and statistics.

3. What are the different methods of integration?

The main methods of integration are the substitution method, the integration by parts method, and the partial fractions method. These methods allow us to evaluate integrals that are difficult or impossible to solve using basic integration rules.

4. What is the difference between definite and indefinite integration?

Indefinite integration involves finding the most general antiderivative of a function, while definite integration involves finding the exact value of an integral over a specific interval. In other words, indefinite integration results in a function, while definite integration results in a number.

5. How can I improve my integration skills?

To improve your integration skills, it is important to have a strong understanding of basic integration rules and techniques, as well as practice solving a variety of integration problems. You can also seek help from a tutor or use online resources such as practice problems and video tutorials.

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