Integrating Inverse Trigonometric Functions

This video tutorial covers integral calculus, focusing on integrals leading to inverse trigonometric functions. It includes detailed examples demonstrating the use of arc sine, arc tangent, and arc secant functions to solve integrals. Techniques such as u-substitution and completing the square are employed to facilitate the integration process.

What is the focus of the lecture in this video?

• Linear algebra

• Probability and statistics

• Integral calculus leading to inverse trigonometric functions

• Differential calculus

Which derivative is equal to du over the square root of one minus u squared?

• Arc cosine

• Arc tangent

• Arc secant

• Arc sine

What is the integral of du over a squared plus u squared?

• Arc sine of u over a

• Arc tangent of u over a

• Arc secant of u over a

• Arc cosine of u over a

In the example of integrating dx over the square root of 3 minus x squared, what is the resulting function?

• Arc sine

• Arc cosine

• Arc secant

• Arc tangent

What is the value of a squared in the example of integrating dx over 4x squared plus 9?

• 25

• 16

• 9

• 4

In the example of integrating dy over y times the square root of 3y squared minus 25, what is the resulting function?

• Arc tangent

• Arc sine

• Arc secant

• Arc cosine

What is the value of a in the example of integrating secant squared theta over 16 minus tangent squared theta?

• 2

• 5

• 3

• 4

In the example of integrating x dx over 7 plus x to the 4, what is the resulting function?

• Arc tangent

• Arc secant

• Arc sine

• Arc cosine

What is the value of a squared in the example of integrating dx over x plus x ln squared x?

• 1

• 4

• 2

• 3

In the example of integrating x plus 1 over x squared plus 4, what two functions are involved?

• Arc cosine and ln

• Arc sine and ln

• Arc tangent and ln

• Arc secant and ln