Trigonometric integral problem

In summary, a trigonometric integral problem involves finding the integral of a function containing trigonometric functions. Common strategies for solving these problems include using identities, substitution, and integration by parts. There is a difference between definite and indefinite trigonometric integrals, as the former has specific limits of integration while the latter does not. Trigonometric integral problems can be solved using calculators or computer programs, but it is important to understand the concepts behind them. These problems have real-world applications in fields such as physics, engineering, and economics.
  • #1
sahen
7
0

Homework Statement


[tex]\int\frac{1+\sqrt{cosx}}{sinx}[/tex] Hi , I really need a help for this


Homework Equations





The Attempt at a Solution



[tex]\int\frac{1+\sqrt{cosx}}{\sqrt{sin}\sqrt{sin}}[/tex]

[tex]\int\frac{1}{sinx}[/tex] + [tex]\int\frac{1}{\sqrt{sinx}}\sqrt{}\frac{cosx}{sinx}[/tex] =

[tex]\int cscx[/tex] + [tex]\int\sqrt{cscx cotx}[/tex] = ?

[tex]\int cscx[/tex] is alright but i have no idea for second part .

do you have any idea ?
 
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  • #2
Make the substitution [tex]\sqrt{cosx}=a[/tex] Then simplify the resulting expression, use partial fractions and you're done.
 
  • #3
Yes that's it! thanks for your help...
 

What is a trigonometric integral problem?

A trigonometric integral problem involves finding the integral (or antiderivative) of a function that contains trigonometric functions such as sine, cosine, tangent, etc.

What are some common strategies for solving trigonometric integral problems?

Some common strategies include using trigonometric identities, substitution, and integration by parts.

What is the difference between a definite and indefinite trigonometric integral?

A definite trigonometric integral has specific limits of integration, while an indefinite trigonometric integral does not. This means that a definite integral will result in a numerical value, while an indefinite integral will result in a function.

Can trigonometric integral problems be solved using a calculator or computer program?

Yes, many calculators and computer programs have the capability to solve trigonometric integral problems. However, it is still important to understand the concepts and strategies behind solving these problems.

Are there any real-world applications of trigonometric integral problems?

Yes, trigonometric integral problems are used in fields such as physics, engineering, and economics to model and solve various real-world problems involving trigonometric functions.

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