U substitution with trig sine and cosine

The video tutorial explains the process of taking derivatives of sine functions, focusing on the transition from sine to cosine. It introduces the concept of U-substitution, using sine of 3X as an example, and discusses the need to adjust the derivative by multiplying with a constant. The tutorial concludes with the integration process, replacing variables, and finalizing the solution.

What is the derivative of sine?

• Tangent

• Cosine

• Cosecant

• Secant

In the substitution method, what is 'U' defined as?

• Secant of 3X

• Sine of 3X

• Cosine of 3X

• Tangent of 3X

What adjustment is made to account for the constant factor in the derivative of U?

• Multiply by 2

• Divide by 3

• Multiply by 1/3

• Add 3

What is the final expression obtained after integration?

• 1/12 sine of 3X raised to the 4th power plus C

• 1/3 cosine of 3X raised to the 3rd power plus C

• 1/3 sine of 3X raised to the 3rd power plus C

• 1/12 cosine of 3X raised to the 4th power plus C

What is the purpose of replacing 'U' back with sine in the integration process?

• To simplify the expression

• To find the derivative

• To complete the integration

• To eliminate constants