lct10 Double integr. in polar coörds

What is the formula of a closed disk in kartesian and polar coördinates?

• kartesian: x² + y² = k

• polar: r² = k

What are the polar transformations for x and y?

• x = rcos(theta)

• y = rsin(theta)

What is the term dA for a double integral in polar coords?

r dr dtheta

What is the integral of function f(x, y) in this domain?

What does a bounded region in polar coörds with fixed limits for r look like?

Not tested in exam!!!!!!!!!

What does a bounded region in polar coörds with fixed limits for theta look like?

What is D, and the integral of f(x,y) n polar coörds with fixed limits of theta?

Give algorithm for solving a double integral with polar coörds with only fixed limits for theta.

1. Draw region

2. Solve (if nessicary) boundary intersect r1 = r2, this gives theta1 & theta2

3. Rewrite f(x,y) to polar coörds

4. Solve integral

Give formula for a thin flat object in the x-y plane with mass density sigma(x, y):

• around x-axis

• around y-axis

• around origin