Integral of a function gives me acrtan(2cot(x)). How to evaluate this?

In summary, the conversation discusses the integration of a power function with respect to time and the evaluation of this integral between the limits of 0 and 60. The solution provided by Wolframalpha involves a constant, which was initially forgotten but later recognized. The value of 0 in the limits raises a question about the physics of the equation as it results in an infinite value for cot(x).
  • #1
anj16
38
0
Function is context is:
$$\int \frac{(sin^22x)}{(4(1+3cos^2(x)))}dx$$

And according to wolframalpha (I wasn't able to integrate this by myself) this integral is equal to

$$\frac{5 x}{18} + \frac{(2 arctan(2 cot(x)))}{9} - \frac{sin(2 x)}{12}$$

The above integral is the integral of a power function with respect to time.
And I wanted to evaluate this between [0,60]; but the problem is when evaluating the cot(x) at 0 this give me infinity which make the fraction in the middle ∏/9. But according to the physics of the equation there should not be any energy generated at time = 0 as nothing is happening at time 0. so what is going on??

Thanks!
 
Last edited:
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  • #2
Plus a constant... and what you've done is figure out what that constant is
 
  • #3
What does [0,60] represent? Does it have units?
 
  • #4
SteamKing said:
What does [0,60] represent? Does it have units?

Not trying to be rude but in my original post I said "integrating with respect to time" so I didn't type time again; I thought it would be unnecessary.
 
  • #5
Office_Shredder said:
Plus a constant... and what you've done is figure out what that constant is

That makes sense. I completely forgot about the constant. Thanks!
 

FAQ: Integral of a function gives me acrtan(2cot(x)). How to evaluate this?

What is the definition of an integral?

An integral is a mathematical concept that represents the area under a curve on a graph. It is used to find the total value of a function between two given points.

How do I evaluate an integral?

To evaluate an integral, you can use various techniques such as substitution, integration by parts, or partial fractions. You can also use online calculators or software programs to evaluate integrals.

What is acrtan(2cot(x))?

Acrtan(2cot(x)) is a trigonometric function that represents the inverse tangent of 2 times the cotangent of x. It is commonly used in calculus and is equivalent to arctan(2/tan(x)).

How do I simplify acrtan(2cot(x)) to evaluate the integral?

To simplify acrtan(2cot(x)), you can use trigonometric identities such as tan(x) = sin(x)/cos(x) and cot(x) = cos(x)/sin(x). This will help you rewrite the function in a more manageable form.

Is there a specific method for evaluating integrals involving inverse trigonometric functions?

Yes, there are specific methods for evaluating integrals involving inverse trigonometric functions such as using trigonometric identities, substitution, or integration by parts. It is important to choose the most suitable method for each specific integral to obtain an accurate solution.

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