Integrating Trigonometric Functions

The video tutorial explains how to integrate trigonometric functions using u-substitution, focusing on cosine functions with linear angles. It provides a general method for integrating sine and cosine functions when the angle is a linear function. The tutorial includes examples and practice problems for integrating sine, secant squared, and secant functions, emphasizing the importance of dividing by the derivative of the angle.

What is the first step in using u-substitution to integrate cosine 2x?

• Set u equal to 2x

• Find the derivative of cosine

• Set u equal to cosine 2x

• Find the antiderivative of sine

What is the antiderivative of cosine?

• Secant

• Cosine

• Sine

• Tangent

What is the derivative of sine?

• Negative sine

• Cosine

• Negative cosine

• Sine

How do you integrate cosine 3x using the general process?

• Sine 3x divided by 3

• Cosine 3x divided by 3

• Sine 3x times 3

• Cosine 3x times 3

What is the integral of cosine 4x?

• Sine 4x times 4

• Cosine 4x over 4

• Cosine 4x times 4

• Sine 4x over 4

What is the integral of cosine 7x minus 5?

• Sine 7x minus 5 over 7

• Cosine 7x minus 5 over 7

• Sine 7x minus 5 times 7

• Cosine 7x minus 5 times 7

What is the integral of sine 6x?

• Cosine 6x over 6

• Negative cosine 6x over 6

• Negative sine 6x over 6

• Sine 6x over 6

What is the integral of secant squared 9x plus 3?

• Four times tangent 9x plus 3 over 9

• Tangent 9x plus 3 over 9

• Four times secant 9x plus 3 over 9

• Secant 9x plus 3 over 9

What is the integral of 5 secant 3x tangent 3x?

• Secant 3x over 3

• Five times tangent 3x over 3

• Tangent 3x over 3

• Five times secant 3x over 3

What is the integral of secant squared?

• Tangent

• Sine

• Cosine

• Secant