Volume Calculation Using the Washer Method

The video tutorial explains the washer method for calculating the volume of a solid of revolution. It begins by setting up the definite integral and factoring out pi. The expression is then simplified, and the antiderivative is calculated. Finally, the integral is evaluated at specific points to determine the volume, resulting in a final value of 31 pi over 30.

What method is introduced for calculating the volume of a solid of revolution?

• Cavalieri's Principle

• Disk Method

• Shell Method

• Washer Method

What is the first step in simplifying the integral for volume calculation?

• Changing the limits of integration

• Factoring out pi

• Expanding the terms

• Differentiating the expression

Which term is the highest degree in the expression before integration?

• y squared

• y to the fourth

• y to the half

• y to the third

Which term in the expression becomes positive due to a double negative?

• y to the half

• y to the fourth

• 4 square roots of y

• y squared

What is the antiderivative of y to the fourth?

• y to the sixth over 6

• y to the fourth over 4

• y to the fifth over 5

• y to the third over 3

What happens to the integral when evaluated at the lower bound of 0?

• It equals zero

• It doubles

• It equals one

• It becomes undefined

What is the antiderivative of negative y?

• Negative y squared over 2

• Negative y to the fifth over 5

• Negative y to the fourth over 4

• Negative y cubed over 3

What is the antiderivative of 4 y to the 1/2?

• 8/3 y to the 3/2

• 4/3 y to the 3/2

• 6/3 y to the 3/2

• 2/3 y to the 3/2

What is the least common multiple used to simplify the fractions in the final step?

• 20

• 25

• 35

• 30

What is the final simplified volume of the solid?

• 31 pi over 25

• 31 pi over 20

• 31 pi over 35

• 31 pi over 30