Mass Calculation of a Two-Dimensional Hockey Puck

The video tutorial explains how to calculate the mass of a two-dimensional oversized hockey puck with a given density function. It begins by setting up the problem and explaining the integral needed to find the mass. The tutorial then walks through the process of finding the antiderivative of the function and evaluating the integral to determine the exact mass. Finally, it concludes with the exact and approximate mass values, emphasizing the importance of providing exact values unless otherwise instructed.

What is the radius of the hockey puck mentioned in the problem?

• 3 inches

• 6 inches

• 4 inches

• 5 inches

What is the formula used to calculate the mass of the disk?

• Integral from 0 to r of 4 pi x times rho of x dx

• Integral from 0 to r of 3 pi x times rho of x dx

• Integral from 0 to r of 2 pi x times rho of x dx

• Integral from 0 to r of pi x times rho of x dx

What is the density function used in the integral setup?

• x squared minus x plus 2

• x cubed minus x plus 2

• x cubed minus 2x plus 3

• x squared minus 2x plus 3

What is the antiderivative of x to the fourth minus two x squared plus 3x?

• 1/5 x to the fifth minus 2/3 x cubed plus 3/2 x squared

• 1/4 x to the fourth minus 2/2 x squared plus 3/3 x

• 1/6 x to the sixth minus 2/4 x cubed plus 3/5 x squared

• 1/3 x to the third minus 2/5 x squared plus 3/4 x

What is the value of the mass when x is 0?

• All terms are 0

• All terms are 10

• All terms are 1

• All terms are 5

What is the exact mass of the hockey puck?

• 3,075 divided by 5 pi

• 3,075 divided by 4 pi

• 3,075 divided by 3 pi

• 3,075 divided by 2 pi

What should be done if the directions do not indicate rounding?

• Always give the approximate value

• Always give the estimated value

• Always give the exact value

• Always round the value