Integration by Parts and Inverse Trigonometric Functions

The video tutorial explains how to integrate the sine inverse function using integration by parts. It begins with an introduction to inverse trigonometric functions, emphasizing that the minus one notation is not an exponent but indicates an inverse function. The tutorial then sets up the integration by parts process, treating sine inverse as a product with one. It proceeds with the integration, using substitution to simplify the integral, and concludes with the final steps to reach the solution. The video provides a clear, step-by-step approach to solving integrals involving inverse trigonometric functions.

What is the correct interpretation of the notation sin^(-1)(X)?

• sin(X)^-1

• arcsin(X)

• cos(X)

• 1/sin(X)

Which of the following is NOT true about inverse trigonometric functions?

• They are also known as arc functions.

• The notation -1 indicates an inverse function, not an exponent.

• They can be expressed as 1 over the trigonometric function.

• They are used to find angles from trigonometric ratios.

What is the first step in using integration by parts for sin^(-1)(X)?

• Set DV as sin^(-1)(X) and U as 1*dx

• Integrate sin^(-1)(X)

• Set U as sin^(-1)(X) and DV as 1*dx

• Differentiate sin^(-1)(X)

In the integration by parts method, what is the derivative of sin^(-1)(X)?

• 1/sqrt(1 + X^2)

• 1/sqrt(1 - X^2)

• 1/(1 - X^2)

• 1/(1 + X^2)

What is the formula for integration by parts?

• UV + integral of VDU

• U/V - integral of VDU

• UV - integral of VDU

• U/V + integral of VDU

After setting up integration by parts, what expression do we get for the integral of sin^(-1)(X)?

• X * sin^(-1)(X) + integral of X/sqrt(1 - X^2) dx

• X * sin^(-1)(X) - integral of X/sqrt(1 - X^2) dx

• X * sin^(-1)(X) - integral of 1/sqrt(1 - X^2) dx

• X * sin^(-1)(X) + integral of 1/sqrt(1 - X^2) dx

What substitution is used to simplify the integral of X/sqrt(1 - X^2)?

• Let W = 1 + X^2

• Let W = sqrt(1 - X^2)

• Let W = 1 - X^2

• Let W = X^2

What is the derivative of W when W = 1 - X^2?

• X dx

• 2X dx

• -X dx

• -2X dx

How is the integral of 1/sqrt(W) rewritten for easier integration?

• W^(2)

• W^(-2)

• W^(1/2)

• W^(-1/2)

What is the final expression for the integral of sin^(-1)(X) dx?

• X * sin^(-1)(X) + sqrt(1 - X^2) + C

• X * sin^(-1)(X) - sqrt(1 - X^2) + C

• X * sin^(-1)(X) + 1/(1 - X^2) + C

• X * sin^(-1)(X) - 1/(1 - X^2) + C