Volumes in spherical coordinates Use integration in spherical coordinates to find the volume of the following solids . 49. The solid rose petal of revolution D = { ( ρ , φ , θ ) : 0 ≤ ρ ≤ 4 sin 2 φ , 0 ≤ φ π / 2 , 0 ≤ θ ≤ 2 π }
Volumes in spherical coordinates Use integration in spherical coordinates to find the volume of the following solids . 49. The solid rose petal of revolution D = { ( ρ , φ , θ ) : 0 ≤ ρ ≤ 4 sin 2 φ , 0 ≤ φ π / 2 , 0 ≤ θ ≤ 2 π }
Solution Summary: The author explains how the volume of the given solid in spherical coordinates is given by, V=displaystyle undersetDiiint
Volumes in spherical coordinatesUse integration in spherical coordinates to find the volume of the following solids.
49. The solid rose petal of revolution
D
=
{
(
ρ
,
φ
,
θ
)
:
0
≤
ρ
≤
4
sin
2
φ
,
0
≤
φ
π
/
2
,
0
≤
θ
≤
2
π
}
With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.
Use Cylindrical Coordinates to find the volume of the solid inside the hemisphere
36-x - y and inside the cylinder x² + y² =9 above the xy plane. Exact Volume Only
z =
Use cylindrical coordinates to find the volume of the solid.
Solid inside x² + y² + z² = 16 and outside z =
2
+ y²
The equation of a three-dimensional figure in rectangular coordinates along with
its sketch are shown below. Which among the following is the correct integral
expression for the volume of the space bound by the surface and the through-
origin axis planes as shown in cylindrical coordinates?
x? + 2y? + 2z – 5 = 0
y
Sz- (cos 0 2(sin 0)*)
sin
V5
rdrdedr
5-2z
(cas 0)+2(sin )2)
S S So
rdrdodz
rv5 p5 v2(cos ' 5)° 5z (cos 0)°_2(sin 0)*)
So
rdrdodx
5 cos 0- 2y
V2 sin 1
So
rdrdedy
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.
Area Between The Curve Problem No 1 - Applications Of Definite Integration - Diploma Maths II; Author: Ekeeda;https://www.youtube.com/watch?v=q3ZU0GnGaxA;License: Standard YouTube License, CC-BY