Name  ________________         BC Calculus Takehome Test      Date ______________     

Note:

A. You must show all your work on each problem to get full credit.

B. You may use your calculator only for numerical calculation and graphing.

C. You may use your notes, but you may not use any (other) human resource.

Problem 1.  Find the arc length and the surface area (rotate about the y-axis).

x(t) = 3*t^2, `  `*y(t) = 2*t^3, `  `*t = 0 .. 3

Problem 2.  Find the arc length and the surface area (rotate about the x-axis).

x(t) = 5*cos(t)^3, `  `*y(t) = 5*sin(t)^3, `  `*t = -1/2*Pi .. 1/2*Pi

Problem 3.  Find the arc length and the surface area (rotate about the y-axis).

x(t) = exp(t)+exp(-t), `  `*y(t) = 5-2*t, `  `*t = 0 .. 2

Problem 4.  Find a formula for the antiderivative and check by taking the derivative.

Int((a^2-u^2)^(1/2)/u,u), `  a is a nonzero constant.`

Problem 5.  Find a formula for the antiderivative and check by taking the derivative.

Int(u^2/(u^2-a^2)^(1/2),u), `  a is a nonzero constant.`