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    Mathematics
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    Calculus A Complete Course
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    Exam 18: Differential Forms and Exterior Calculus
  5. Question
    Let Ω Be the Differential 3-Form Be\(\pi\)
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Let Ω Be the Differential 3-Form Be π\piπ

Question 48

Question 48

Multiple Choice

Let Ω be the differential 3-form    Let Ω be the differential 3-form     be the 4-dimensional ball of radius α in R<sup>4</sup> ; that is     (a)  Use the generalized Stokes's Theorem to evaluate     (b)  Use part (a)  to find the 4-volume of the ball. Hint: You may use symmetry and the transformation  ,  .     A)  4 \pi    B)        C)        D)  2     E)     \pi   be the 4-dimensional ball of radius α in R4 ; that is
   Let Ω be the differential 3-form     be the 4-dimensional ball of radius α in R<sup>4</sup> ; that is     (a)  Use the generalized Stokes's Theorem to evaluate     (b)  Use part (a)  to find the 4-volume of the ball. Hint: You may use symmetry and the transformation  ,  .     A)  4 \pi    B)        C)        D)  2     E)     \pi
(a) Use the generalized Stokes's Theorem to evaluate    Let Ω be the differential 3-form     be the 4-dimensional ball of radius α in R<sup>4</sup> ; that is     (a)  Use the generalized Stokes's Theorem to evaluate     (b)  Use part (a)  to find the 4-volume of the ball. Hint: You may use symmetry and the transformation  ,  .     A)  4 \pi    B)        C)        D)  2     E)     \pi
(b) Use part (a) to find the 4-volume of the ball.
Hint: You may use symmetry and the transformation , .
   Let Ω be the differential 3-form     be the 4-dimensional ball of radius α in R<sup>4</sup> ; that is     (a)  Use the generalized Stokes's Theorem to evaluate     (b)  Use part (a)  to find the 4-volume of the ball. Hint: You may use symmetry and the transformation  ,  .     A)  4 \pi    B)        C)        D)  2     E)     \pi


A) 4 π\piπ    Let Ω be the differential 3-form     be the 4-dimensional ball of radius α in R<sup>4</sup> ; that is     (a)  Use the generalized Stokes's Theorem to evaluate     (b)  Use part (a)  to find the 4-volume of the ball. Hint: You may use symmetry and the transformation  ,  .     A)  4 \pi    B)        C)        D)  2     E)     \pi
B)    Let Ω be the differential 3-form     be the 4-dimensional ball of radius α in R<sup>4</sup> ; that is     (a)  Use the generalized Stokes's Theorem to evaluate     (b)  Use part (a)  to find the 4-volume of the ball. Hint: You may use symmetry and the transformation  ,  .     A)  4 \pi    B)        C)        D)  2     E)     \pi      Let Ω be the differential 3-form     be the 4-dimensional ball of radius α in R<sup>4</sup> ; that is     (a)  Use the generalized Stokes's Theorem to evaluate     (b)  Use part (a)  to find the 4-volume of the ball. Hint: You may use symmetry and the transformation  ,  .     A)  4 \pi    B)        C)        D)  2     E)     \pi      Let Ω be the differential 3-form     be the 4-dimensional ball of radius α in R<sup>4</sup> ; that is     (a)  Use the generalized Stokes's Theorem to evaluate     (b)  Use part (a)  to find the 4-volume of the ball. Hint: You may use symmetry and the transformation  ,  .     A)  4 \pi    B)        C)        D)  2     E)     \pi
C)    Let Ω be the differential 3-form     be the 4-dimensional ball of radius α in R<sup>4</sup> ; that is     (a)  Use the generalized Stokes's Theorem to evaluate     (b)  Use part (a)  to find the 4-volume of the ball. Hint: You may use symmetry and the transformation  ,  .     A)  4 \pi    B)        C)        D)  2     E)     \pi      Let Ω be the differential 3-form     be the 4-dimensional ball of radius α in R<sup>4</sup> ; that is     (a)  Use the generalized Stokes's Theorem to evaluate     (b)  Use part (a)  to find the 4-volume of the ball. Hint: You may use symmetry and the transformation  ,  .     A)  4 \pi    B)        C)        D)  2     E)     \pi      Let Ω be the differential 3-form     be the 4-dimensional ball of radius α in R<sup>4</sup> ; that is     (a)  Use the generalized Stokes's Theorem to evaluate     (b)  Use part (a)  to find the 4-volume of the ball. Hint: You may use symmetry and the transformation  ,  .     A)  4 \pi    B)        C)        D)  2     E)     \pi
D) 2    Let Ω be the differential 3-form     be the 4-dimensional ball of radius α in R<sup>4</sup> ; that is     (a)  Use the generalized Stokes's Theorem to evaluate     (b)  Use part (a)  to find the 4-volume of the ball. Hint: You may use symmetry and the transformation  ,  .     A)  4 \pi    B)        C)        D)  2     E)     \pi      Let Ω be the differential 3-form     be the 4-dimensional ball of radius α in R<sup>4</sup> ; that is     (a)  Use the generalized Stokes's Theorem to evaluate     (b)  Use part (a)  to find the 4-volume of the ball. Hint: You may use symmetry and the transformation  ,  .     A)  4 \pi    B)        C)        D)  2     E)     \pi
E)    Let Ω be the differential 3-form     be the 4-dimensional ball of radius α in R<sup>4</sup> ; that is     (a)  Use the generalized Stokes's Theorem to evaluate     (b)  Use part (a)  to find the 4-volume of the ball. Hint: You may use symmetry and the transformation  ,  .     A)  4 \pi    B)        C)        D)  2     E)     \pi   π\piπ    Let Ω be the differential 3-form     be the 4-dimensional ball of radius α in R<sup>4</sup> ; that is     (a)  Use the generalized Stokes's Theorem to evaluate     (b)  Use part (a)  to find the 4-volume of the ball. Hint: You may use symmetry and the transformation  ,  .     A)  4 \pi    B)        C)        D)  2     E)     \pi

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