Trigonometric Identities and Integrals

The video tutorial explains how to find the indefinite integral of 1 over the square root of 1 minus x squared using trigonometric substitution. The process involves substituting x with the sine function and using the Pythagorean identity to simplify the integral. The tutorial then solves the integral, resulting in the arc sine of x plus a constant. Key concepts include trigonometric substitution, Pythagorean identity, and inverse functions.

What is the integral of 1 over the square root of 1 minus x squared?

• tangent of x

• arc sine of x

• cosine of x

• x squared

Which trigonometric function is used to replace x in the substitution process?

• Sine

• Secant

• Cosine

• Tangent

What is the derivative of sine u with respect to u?

• Sine u

• Secant u

• Cosine u

• Tangent u

Which identity is used to simplify the expression 1 minus sine squared?

• Sine squared plus tangent squared equals one

• Sine squared plus secant squared equals one

• Cosine squared plus sine squared equals one

• Tangent squared plus secant squared equals one

What does the expression 1 over the square root of cosine squared simplify to?

• One

• Cosine

• Sine

• Zero

What is the integral of 1 with respect to u?

• sine of u

• cosine of u

• u squared

• u plus a constant

If x equals sine of u, what is u in terms of x?

• Arc secant of x

• Arc cosine of x

• Arc sine of x

• Arc tangent of x

What is the final result of the integral in terms of x?

• Arc secant of x plus a constant

• Arc sine of x plus a constant

• Arc tangent of x plus a constant

• Arc cosine of x plus a constant

What is the purpose of switching x and u when dealing with inverse functions?

• To integrate the function

• To solve for the original variable

• To find the derivative

• To simplify the equation

What is the constant of integration typically represented by?

• D

• C

• B

• A