Double Integrals and Polar Coordinates

The video tutorial explains how to evaluate a double integral over a specified region, which is a circle in the xy-plane. The function is constant, and the integral represents the volume under the surface. The process involves converting the integral to polar coordinates, finding limits of integration, and performing the integration. The result is verified using a geometric formula for the volume of a cylinder.

What is the shape of the region of integration in the given problem?

• An ellipse

• A square

• A circle

• A triangle

What does the double integral represent in this context?

• The perimeter of a circle

• The length of a curve

• The volume under a surface

• The area of a rectangle

Tags

CCSS.HSN.CN.B.4

What is the function f(x, y) equal to in this problem?

• 9

• 7

• x^2 + y^2

• x + y

Tags

CCSS.HSN.CN.B.4

When converting to polar coordinates, what additional factor must be included in the differential?

• y

• r

• theta

• x

What are the limits of integration for r in polar coordinates?

• 0 to 3

• 0 to 2

• 0 to 4

• 0 to 1

Tags

CCSS.HSG.GMD.A.3

CCSS.8.G.C.9

What is the result of the double integral in terms of pi?

• 31.5 pi

• 63 pi

• 126 pi

• 94.5 pi

Tags

CCSS.2.G.A.1

CCSS.1.G.A.1

What is the height of the right circular cylinder in this problem?

• 9

• 5

• 3

• 7

What is the radius of the base of the cylinder?

• 2

• 3

• 1

• 4

Tags

CCSS.HSG.GMD.A.3

CCSS.8.G.C.9

Which formula is used to verify the volume of the cylinder?

• Area of a circle

• Volume of a sphere

• Surface area of a cylinder

• Volume of a right circular cylinder

What is the approximate decimal value of the volume found?

• 250.4321

• 150.5678

• 200.1234

• 197.9203