136.275, Assignment No. 6

March 17, 2003

The assignment is due Monday, March 24 in class. Late assignments receive a mark zero.

1. a) In evaluating a double integral over a region G, a sum of two integrals was obtained as follows:

.

Sketch the region G and express the double integral as an iterated integral with

reversed order of integration. [6]

b) Calculate the integral for f(x,y) = by using a). [6]

2. Find the surface area of the portion of the cylinder that is above the

rectangle R = [0,2] X [-3,3] . [7]

3. Rewrite the integral as integral in dz dx dy and then dy dx dz.

(A sketch of the solid and of the regions in xy and xz planes will help.) [9]

4. Question No. 38 on page 1075 of the textbook. [9]

5. Show that , where the improper triple

integral is defined as the limit of a triple integral over a solid sphere as the radius

of the sphere increases indefinitely. [7]

Total [ 44/42]