Question

If you integrate with (R=[1,3]×[1,2]) WTD? Ex: (int 1)/1+x+y) ,dx)?

a. Double integration
b. Triple integration
c. Line integration
d. Surface integration

Answer 1

The integration over the region R=[1,3]×[1,2] is a double integration because it involves integrating over an area in two dimensions, not a volume or along a path.

Step-by-step explanation:

The integration involved with the region R=[1,3]\times[1,2] would be a double integration. This is because the region R is a rectangle in the xy-plane, and so we are integrating over an area in two dimensions, not a volume in three dimensions nor along a line or over a surface. Double integration allows us to calculate the volume under the surface defined by the function f(x,y) over the region R.

Let's consider an example similar to the one provided, \int\int_R \frac{1} {1 + x + y} dxdy. Here, you would integrate with respect to x from 1 to 3 and with respect to y from 1 to 2 in either order due to Fubini's Theorem, since the limits of integration are constants.