In some cases it is possible to use Definition 15.5.1 along with symmetry considerations to evaluate a surface integral without reference to a parametrization of the surface. In these exercises, σ denotes the unit sphere centered at the origin. Use the results of Exercises 16 and 17 to evaluate ∬ σ x − y 2 d S without performing an integration .
In some cases it is possible to use Definition 15.5.1 along with symmetry considerations to evaluate a surface integral without reference to a parametrization of the surface. In these exercises, σ denotes the unit sphere centered at the origin. Use the results of Exercises 16 and 17 to evaluate ∬ σ x − y 2 d S without performing an integration .
In some cases it is possible to use Definition 15.5.1 along with symmetry considerations to evaluate a surface integral without reference to a parametrization of the surface. In these exercises,
σ
denotes the unit sphere centered at the origin.
Use the results of Exercises 16 and 17 to evaluate
∬
σ
x
−
y
2
d
S
without performing an integration.
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.
Find a parametrization of the surface x³ + 15xy + z² = 10 where x > 0 and use it to find the tangent plane at
1
x = 2, y =
15
(Use symbolic notation and fractions where needed.)
y =
, Z = 0.
Find a parametrization of the osculating circle for the parabola y = x2 when x = 1
A light bulb is designed by revolving the graph of y = tzi - rł, o
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.