Antiderivatives of Inverse Trigonometric Functions

This video tutorial covers the process of finding antiderivatives of inverse trigonometric functions. It begins with an introduction to key formulas for arcsin, arctangent, and arcsecant functions. The tutorial then provides detailed examples, demonstrating how to apply these formulas to solve various antiderivative problems, including complex cases and using methods like long division. The video aims to enhance understanding of calculus concepts related to inverse trigonometric functions.

What is the main focus of the video tutorial?

• Graphing functions

• Finding antiderivatives of inverse trigonometric functions

• Solving algebraic equations

• Finding derivatives of trigonometric functions

Which formula is used for the antiderivative of vu over the square root of a square minus u square?

• arctangent u over a plus C

• arccos u over a plus C

• arcsin u over a plus C

• arcsecond u over a plus C

In Example 1, what is the value of 'a' when finding the antiderivative of x over the square root of 16 minus x squared?

• 2

• 3

• 4

• 5

What is the final answer for the antiderivative in Example 1?

• arccos x over 4 plus C

• arcsin x over 4 plus C

• arctangent x over 4 plus C

• arcsecond x over 4 plus C

In Example 2, what is the value of 'a' when finding the antiderivative of 3 over 25 plus x squared?

• 7

• 4

• 5

• 6

What is the final answer for the antiderivative in Example 2?

• 3 over 5 arcsecond x over 5 plus C

• 3 over 5 arcsin x over 5 plus C

• 3 over 5 arccos x over 5 plus C

• 3 over 5 arctangent x over 5 plus C

In Example 3, what is the value of 'a' when finding the antiderivative of 8 over x times the square root of 4x squared minus 1?

• 1

• 2

• 3

• 4

What is the final answer for the antiderivative in Example 3?

• 8 arcsin 2x plus C

• 8 arctangent 2x plus C

• 8 arcsecond 2x plus C

• 8 arccos 2x plus C

In Example 4, what is the value of 'a' when finding the antiderivative of x over the square root of 1 minus x raised to the fourth power?

• 4

• 3

• 2

• 1

What is the final answer for the antiderivative in Example 4?

• 1/2 arctangent x squared plus C

• 1/2 arcsin x squared plus C

• 1/2 arccos x squared plus C

• 1/2 arcsecond x squared plus C