Integration of Inverse Trigonometric Functions

The video tutorial covers inverse trigonometric functions, starting with a review of tan inverse and its proof. It then explores the relationship between sin inverse and cos inverse, particularly focusing on their gradients. The tutorial also discusses the application of the chain rule in differentiating these functions and concludes with an introduction to integration and practice exercises.

What is the result of the derivative of tan inverse?

• x / (1 + x^2)

• 1 / (1 - x^2)

• 1 / (1 + x^2)

• x / (1 - x^2)

What is the expression under the square root in the derivative of sin inverse?

• 1 + x^2

• 1 - x^2

• x^2 - 1

• x^2 + 1

How do the gradients of sin inverse and cos inverse relate to each other?

• Both are always increasing

• Both are always decreasing

• They are unrelated

• One is increasing while the other is decreasing

What happens to the gradient of sin inverse at x = 0?

• It is -1

• It is 1

• It is 0

• It is undefined

What is the effect of applying the chain rule to the derivative of an inverse trigonometric function?

• It has no effect

• It multiplies the derivative of the inside function

• It changes the denominator

• It adds a constant to the numerator

In the chain rule application, what replaces 'x' in the denominator?

• The function itself

• The square of the function

• The derivative of the inside function

• The original function

What is the first step in integrating inverse trigonometric functions?

• Simplify the function

• Apply the chain rule

• Recognize the form of the function

• Differentiate the function

Which inverse trigonometric function is associated with the form 1 / (1 + x^2)?

• sin inverse

• cos inverse

• sec inverse

• tan inverse

What is the key to mastering integration of inverse trigonometric functions?

• Practicing differentiation

• Understanding limits

• Recognizing patterns

• Memorizing formulas

Which of the following is true about the integration of inverse trigonometric functions?

• It requires recognizing the function's form

• It is only applicable to tan inverse

• It is more complex than differentiation

• It is unrelated to differentiation