Volume Calculation Using Shell Method

The video tutorial explains how to evaluate the volume of a solid of revolution using the shell method. It begins by setting up a definite integral, then simplifies the expression for integration. The process involves taking the antiderivative and evaluating the integral from 0 to 3. The tutorial concludes with the final calculation, resulting in the volume of the shape.

What method is used to evaluate the volume of the solid of revolution in this video?

• Disk Method

• Shell Method

• Washer Method

• Cavalieri's Principle

What is the first step in simplifying the expression?

• Expanding the binomial

• Combining like terms

• Factoring the expression

• Taking the derivative

After expanding the binomial, what is the next step in simplification?

• Factoring out common factors

• Combining like terms

• Adding constants

• Taking the derivative

What is the result of multiplying y plus 2 with the simplified expression?

• Negative y to the fourth power

• Positive y to the third power

• Negative y to the third power

• Positive y to the fourth power

What is taken out of the integral sign to simplify the integration process?

• The constant pi

• The constant 2 pi

• The constant 2

• The variable y

What is the antiderivative of y squared?

• y to the third over 2

• y to the second over 2

• y to the fourth over 4

• y to the third over 3

What is the antiderivative of 6y?

• 3y squared

• 6y squared

• 12y

• y to the third

What is the value of 3 to the fourth power?

• 27

• 81

• 9

• 64

What is the final volume of the solid?

• 81 pi over 4

• 63 pi

• 63 pi over 2

• 144 pi

What is the common denominator used to combine the terms in the final calculation?

• 2

• 3

• 5

• 4