Integral of Sine to the Fourth Power

The video tutorial explains how to find the integral of sine raised to the fourth power of X. It begins by introducing the problem and the necessity of using power reducing formulas. The tutorial then demonstrates how to square the expression and apply the FOIL method to expand it. The integration process is detailed, including simplification steps, and concludes with the final solution, offering options for presenting the answer.

What is the purpose of using power-reducing formulas in this problem?

• To simplify the integration process

• To increase the complexity of the problem

• To avoid using calculus

• To change the function to a different trigonometric function

How can sine to the fourth power be expressed in terms of sine squared?

• As sine squared of X raised to the second power

• As tangent squared of X raised to the second power

• As cosine squared of X raised to the second power

• As cotangent squared of X raised to the second power

Tags

CCSS.7.EE.A.1

What is the result of squaring the fraction 1/2 in the integration process?

• 2

• 1

• 1/2

• 1/4

Tags

CCSS.HSA.APR.A.1

What is the next step after expanding the expression using FOIL?

• Divide by a constant

• Multiply by a constant

• Differentiate the expression

• Combine like terms

Tags

CCSS.HSF.TF.C.9

What is the power-reducing formula for cosine squared?

• 1/2 times (1 + cosine 2x)

• 1/2 times (1 - cosine 2x)

• 1/2 times (1 + sine 2x)

• 1/2 times (1 - sine 2x)

Tags

CCSS.HSF.TF.C.9

Why is it important to double the angle when using the power-reducing formula for cosine squared?

• To maintain the trigonometric identity

• To make the problem more complex

• To avoid using sine

• To simplify the expression

What is the integral of a constant like 3/2?

• 3/2 times X

• 3/2 times X squared

• 3/2 times cosine X

• 3/2 times sine X

What is the integral of cosine 2x?

• Cosine 2x divided by 2

• Cosine 2x multiplied by 2

• Sine 2x multiplied by 2

• Sine 2x divided by 2

Tags

CCSS.HSF.TF.B.7

What is the integral of cosine 4x?

• Sine 4x divided by 4

• Cosine 4x divided by 4

• Sine 4x multiplied by 4

• Cosine 4x multiplied by 4

What is the final expression for the integral of sine to the fourth power of X?

• 1/4 times (3/2x - 1/4 sine 2x + 1/32 sine 4x) + C

• 1/4 times (3/2x + 1/4 sine 2x - 1/32 sine 4x) + C

• 1/4 times (3/2x + 1/2 sine 2x - 1/16 sine 4x) + C

• 1/4 times (3/2x - 1/2 sine 2x + 1/16 sine 4x) + C