Evaluate the surface integral. S x2z2 dS S is the part of the cone z2 = x2 + y2 that lies between the planes z = 3 and z = 4.
Added by Jessica J.
Step 1
We can use cylindrical coordinates to do this. Let x = rcos(θ), y = rsin(θ), and z = z. Then, the surface S is parameterized by r(θ, z) = (rcos(θ), rsin(θ), z) with r ranging from 0 to z and θ ranging from 0 to 2π. The surface element in cylindrical coordinates Show more…
Show all steps
Close
Your feedback will help us improve your experience
Adi S and 100 other Calculus 1 / AB educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Evaluate the surface integral. $$\begin{array}{l}{\iint_{S} x^{2} z^{2} d S} \\ {S \text { is the part of the cone } z^{2}=x^{2}+y^{2} \text { that lies between the }} \\ {\text { planes } z=1 \text { and } z=3}\end{array}$$
VECTOR CALCULUS
Surface Integrals
Use a parametrization to express the area of the surface as a double integral. Then evaluate the integral. The portion of the cone z=3x2+y2 between the planes z=3 and z =6 .
Zack A.
Find the surface area of the given surface. The portion of the cone $z=\sqrt{x^{2}+y^{2}}$ below the plane $z=4$
Vector Calculus
Recommended Textbooks
Calculus: Early Transcendentals
Thomas Calculus
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD