Mass Calculation of a Hockey Puck

The video tutorial explains how to find the mass of a two-dimensional hockey puck with a given density function. It involves setting up a definite integral, using integration by parts, and solving the integral through substitution and simplification. The tutorial concludes with the final calculation of the mass, which is approximately 402.1239.

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

• 6 inches

• 12 inches

• 10 inches

• 8 inches

What is the density function given for the hockey puck?

• rho(x) = 2 + 3 cos(px)

• rho(x) = 3 + 2 cos(px)

• rho(x) = 2 + 3 sin(px)

• rho(x) = 3 + 2 sin(px)

What is the integral setup for calculating the mass of the puck?

• Integral from 0 to 8 of 2x + 3x sec(px) dx

• Integral from 0 to 8 of 2x + 3x tan(px) dx

• Integral from 0 to 8 of 2x + 3x cos(px) dx

• Integral from 0 to 8 of 2x + 3x sin(px) dx

What mathematical technique is used to integrate 3x cos(px) dx?

• Trigonometric Substitution

• Integration by Parts

• Partial Fractions

• Substitution

In integration by parts, what is chosen as 'u' for the integral of 3x cos(px) dx?

• u = 3x

• u = cos(px)

• u = x^2

• u = sin(px)

What substitution is made to integrate cos(px) dx?

• w = px

• w = 3x

• w = x

• w = 2x

What is the antiderivative of 2x with respect to x?

• x^3

• 2x^3

• 2x^2

• x^2

What is the final expression for the antiderivative of the integral?

• x^2 + 3x/pi tan(px) + 3/pi^2 sec(px) + C

• x^2 + 3x/pi cos(px) + 3/pi^2 sin(px) + C

• x^2 + 3x/pi sin(px) + 3/pi^2 cos(px) + C

• x^2 + 3x/pi sec(px) + 3/pi^2 tan(px) + C

What is the exact mass of the hockey puck after evaluating the definite integral?

• 128 pi

• 256 pi

• 32 pi

• 64 pi

What is the approximate numerical value of the mass of the hockey puck?

• 64.1239

• 256.1239

• 128.1239

• 402.1239