In Exercises 65 to 72, find the center and radius of the graph of the circle. The equations of the circles are written in general form. x2 + y2 - 6x - 4y + 12 = 0

Math241 Lecture 8: Double Integrals Now we will be looking at double integrals over general regions without the limits being given to us. Recall that the double integral gives the volume under a particular surface and is equal to ❑ f(x ,y)dA D Ok, let’s look at some examples Examples 5 y 3x+6xydxdy 1. ∫2 2 y This is already set up to be solved so let’s begin. x First, we’ll integrate with respect t. 5 3 2 2 y4 ∫ x +3x y 2dy 2 2 y 5 ∫ 3 y +3y − y −3y dy 5 2 2 2 And now we’ll integrate with respect to . 1 9 3 10 3 5 1 6 5