If parametric equations for a curve are  x=2t and y=t+2, {“version”:”1.1″,”math”:”x=2t and y=t+2, ”} with 0≤t≤5{“version”:”1.1″,”math”:”0≤t≤5″}, what does 2π∫055(t+2)dt{“version”:”1.1″,”math”:”2π∫055(t+2)dt”} represent?

Determine the convergence or divergence of the series ∑n=0∞5-1nn!3n{“version”:”1.1″,”math”:”∑n=0∞5-1nn!3n”}

Evaluate the integral by hand:  ∫sec3ϖtan3ϖdϖ{“version”:”1.1″,”math”:”∫sec3ϖtan3ϖdϖ”}.

Integrate ∫4y2e2ydy{“version”:”1.1″,”math”:”∫4y2e2ydy”}

Set up integral(s) representing the volume of the solid generated by revolving the region bounded by x=0,y=0,y=6{“version”:”1.1″,”math”:”x=0,y=0,y=6″} and y=x-4{“version”:”1.1″,”math”:”y=x-4″} about the line x=10{“version”:”1.1″,”math”:”x=10″}.  a.  Use shells. b.  Use disks/washers. c.  Evaluate one of the integrals.  Record the exact answer, not an approximation.

Set up an integral describing the area inside r=4-4sinθ{“version”:”1.1″,”math”:”r=4-4sinθ”}, and above the line θ=π6{“version”:”1.1″,”math”:”θ=π6″}.  Do not evaluate.

Evaluate the integral by hand:  ∫23x2lnxdx{“version”:”1.1″,”math”:”∫23x2lnxdx”}

Convert x-y=x2+y2{“version”:”1.1″,”math”:”x-y=x2+y2″} to polar coordinates.

After you have completed the exam, you may access your phone to scan the work for problems 19 – 26. Upload the scan in this question.  (Add File.) Then, submit the exam.  Have a great summer!

Find the general solution of the differential equation:  4ydx=x2-4dy{“version”:”1.1″,”math”:”4ydx=x2-4dy”}.  Solve for y.