Let D be the region bounded below the plane z=0, above the sphere x^2 + y^2 + z^2 = 256 , and on the sides by the cylinder x^2 + y^2 = 64 . Set up the triple integrals in cylindrical coordinates that give the volume of D using the following orders of integration. dzdrd?
Added by James H.
Close
Step 1
In cylindrical coordinates, the bounds are: - z is between 0 and sqrt(256 - r^2) - r is between 8 and 16 - θ is between 0 and 2π Show more…
Show all steps
Your feedback will help us improve your experience
Vincenzo Zaccaro and 97 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
Let $D$ be the region bounded below by the plane $z=0,$ above by the sphere $x^{2}+y^{2}+z^{2}=4,$ and on the sides by the cylinder $x^{2}+y^{2}=1 .$ Set up the triple integrals in cylindrical coordinates that give the volume of $D$ using the following orders of integration. a. $d z d r d \theta$ b. $d r d z d \theta$ c. $d \theta d z d r$
Multiple Integrals
Triple Integrals in Cylindrical and Spherical Coordinates
Let $D$ be the region bounded below by the plane $z=0,$ above by the sphere $x^{2}+y^{2}+z^{2}=4,$ and on the sides by the cylinder $x^{2}+y^{2}=1 .$ Set up the triple integrals in cylindrical coordinates that give the volume of $D$ using the following orders of integration. $$ a. d z d r d \theta \quad \text { b. } d r d z d \theta \quad \text { c. } d \theta d z d r $$
Let $D$ be the region bounded below by the planc $z=0,$ above by the sphere $x^{2}+y^{2}+z^{2}=4,$ and on the sides by the cylinder $x^{2}+y^{2}=1 .$ Set up the triple integrals in cylindrical coordi- nates that give the volume of $D$ using the following orders of in- tegration. $$ a.d z d r d \theta \quad \text { b. } d r d z d \theta \quad \text { c. } d \theta d z d r $$
Recommended Textbooks
Calculus: Early Transcendentals
Thomas Calculus
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD