Integral of inverse trigonometric function

In summary, the integral of an inverse trigonometric function is the opposite of the derivative of the trigonometric function and represents the area under the curve of the inverse trigonometric function. It can be found using substitution or integration by parts and is important in calculus for solving problems involving angles and trigonometric functions. There are special rules for integrating inverse trigonometric functions, such as the natural logarithm for arctangent and the argument plus square root for arcsine. Applications of the integral of inverse trigonometric functions include physics, engineering, and finding the area under the curve in practical situations.
  • #1
renob
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Homework Statement


[tex]\int1/sqrt(1-(x+1)^2) dx[/tex]


2. The attempt at a solution
I think a=1 but don't know what to set u equal to.
 
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  • #2
I got it now
 

FAQ: Integral of inverse trigonometric function

What is the definition of the integral of an inverse trigonometric function?

The integral of an inverse trigonometric function is the opposite of the derivative of the trigonometric function. It represents the area under the curve of the inverse trigonometric function.

How do you find the integral of an inverse trigonometric function?

The integral of an inverse trigonometric function can be found by using substitution or integration by parts, depending on the specific function. It is important to use the correct trigonometric identities and to carefully follow the steps of integration.

Why are inverse trigonometric functions important in calculus?

Inverse trigonometric functions are important in calculus because they allow us to find the angles or sides of a triangle when we know the ratios of the sides. They are also used in many real-world applications, such as physics and engineering, to model and solve various problems.

Are there any special rules for integrating inverse trigonometric functions?

Yes, there are a few special rules for integrating inverse trigonometric functions. For example, the integral of arctangent is equal to the natural logarithm of the absolute value of the argument of the arctangent function. Additionally, the integral of arcsine is equal to the argument of the arcsine function plus the square root of one minus the argument squared, all divided by the constant of integration.

What are some common applications of the integral of inverse trigonometric functions?

The integral of inverse trigonometric functions is commonly used in physics, engineering, and other fields to model and solve problems involving angles and trigonometric functions. It is also used in calculus to find the area under the curve of an inverse trigonometric function, which has many practical applications in various industries.

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