Double Integrals II

Part 1. Iterated Double Integrals

Here is the "inert" form of an iterated double integral.

integral := 
      Integrate[Integrate[x*y^2 + x - y, {y, x^2, Sqrt[x]}], {x, 0, 1}]

So far, Mathematica has just "set up" the integral.  It hasn't calculated anything.  If you want to obtain an exact value, you evaluate integral.

integral

On the other hand, if you want a numerical estimate, use N[integral].

N[integral]

Now set up the integral of (x^2) + (y^2) over the region D bounded on the right by the circle of radius 2 centered at the origin and on the left by the line x = 1 as an iterated integral in polar coordinates.  Then use Mathematica to evaluate this integral.

Part 2. Double Integrals Over Coordinate Rectangles

Use the space below to perform your calculation of the exact volume of the tent.  Think carefully about what you need to calculate before you start.

# Calculation of the volume of the tent

Part 3: Double Integrals over More General Regions

Insert your calculations and comments in the spaces below.

# Site 1 calculations

Comments:

# Site 2 calculations

Comments:

Part 4: Summary Report