Reviewing for my Upcoming finals and here are a few questions from early in the

Question

Reviewing for my Upcoming finals and here are a few questions from early in the semester i didnt get correct and would like to know the answers too as well as a some guidance if possible.

Thank you

Consider the following . f(x, y) dy dx = f(x, y) dx dy Determine whether the statement is true or false . If it is false, which of the following shows it is false. (Select all that apply.) f{x, y) = x f{x, y) = y f(x, y ) = x + y f(x, y ) = x - y f(x, y ) = xy The statement is true. Use a double integral in polar coordinates to find the volume of the solid bounded by the graphs of the equations. (Give your answer correct to 2 decimal places.) z = ln(x2 + y2), z = 0, x2 = y2 1, x2 + y2 16

Explanation / Answer

The given statement is true .

Guidance ;

A double integral is something of the form

int int R {f(x, y)} dx dy

where R is called the region of integration and is a region in the (x, y) plane. The

double integral gives us the volume under the surface z = f(x, y), just as a single

integral gives the area under a curve.

*** To evaluate a double integral we do it in stages, starting from the inside and working

out, using our knowledge of the methods for single integrals. The easiest kind of

region R to work with is a rectangle. To evaluate

int int R {f(x, y)} dx dy

proceed as follows:

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