Calculating Volume of Solids

The video tutorial explains how to evaluate a definite integral using the shell method to find the volume of a solid of revolution. It begins by setting up the integral, then expands the expression by multiplying terms. The tutorial proceeds to calculate the antiderivative of the expanded expression and evaluates it at specific limits. Finally, the result is simplified to find the volume of the solid.

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

• Shell method

• Disk method

• Cavalieri's principle

• Washer method

What is the first step in setting up the integral for the shell method?

• Taking the derivative

• Multiplying the expression

• Evaluating the integral

• Finding the limits of integration

How is the expression 2 times the square root of x written for easier integration?

• 2x^1/2

• 2x^1/3

• 2x^2

• 2x^3/2

Which term in the expression is represented as x^3/2?

• Negative x times x^2

• 2 times the square root of x

• Negative x times the square root of x

• 2 times x^2

What is the antiderivative of 2x^1/2?

• 3/2 x^2

• 4/3 x^3/2

• 2/3 x^3/2

• x^2/2

What happens to the terms when evaluated at 0?

• They become negative

• They double

• They cancel out

• They remain unchanged

What is the antiderivative of x^3?

• x^2/2

• x^3/3

• x^4/4

• x^5/5

What is the expression for negative 2/5 x^5/2?

• Negative 2/5 x^5/2

• Positive 2/3 x^3

• Negative 2/3 x^3

• Positive 2/5 x^5/2

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

• 120

• 60

• 90

• 30

What is the final result for the volume of the solid?

• 15π/60

• 31π/30

• 15π/30

• 31π/60