All Calculus 3 Resources
Example Questions
Example Question #1 :年代urface Integrals
Let年代be a known surface with a boundary curve,C.
Considering the integral, utilize Stokes' Theorem to determine an equivalent integral of the form:
In order to utilize Stokes' theorem, note its form
The curl of a vector functionFover an oriented surface年代is equivalent to the functionFitself integrated over the boundary curve,C, of年代.
Note that
From what we're told
Meaning that
From this we can derive our curl vectors
This allows us to set up our surface integral
Example Question #2 :年代urface Integrals
Let年代be a known surface with a boundary curve,C.
Considering the integral, utilize Stokes' Theorem to determine an equivalent integral of the form:
In order to utilize Stokes' theorem, note its form
The curl of a vector functionFover an oriented surface年代is equivalent to the functionFitself integrated over the boundary curve,C, of年代.
Note that
From what we're told
Meaning that
From this we can derive our curl vectors
This allows us to set up our surface integral
Example Question #3 :年代urface Integrals
Let年代be a known surface with a boundary curve,C.
Considering the integral, utilize Stokes' Theorem to determine an equivalent integral of the form:
In order to utilize Stokes' theorem, note its form
The curl of a vector functionFover an oriented surface年代is equivalent to the functionFitself integrated over the boundary curve,C, of年代.
Note that
From what we're told
Meaning that
From this we can derive our curl vectors
This allows us to set up our surface integral
Example Question #4 :年代urface Integrals
Let年代be a known surface with a boundary curve,C.
Considering the integral, utilize Stokes' Theorem to determine an equivalent integral of the form:
In order to utilize Stokes' theorem, note its form
The curl of a vector functionFover an oriented surface年代is equivalent to the functionFitself integrated over the boundary curve,C, of年代.
Note that
From what we're told
Meaning that
From this we can derive our curl vectors
This allows us to set up our surface integral
Example Question #5 :年代urface Integrals
Let年代be a known surface with a boundary curve,C.
Considering the integral, utilize Stokes' Theorem to determine an equivalent integral of the form:
In order to utilize Stokes' theorem, note its form
The curl of a vector functionFover an oriented surface年代is equivalent to the functionFitself integrated over the boundary curve,C, of年代.
Note that
From what we're told
Meaning that
From this we can derive our curl vectors
This allows us to set up our surface integral
Example Question #6 :年代urface Integrals
Let年代be a known surface with a boundary curve,C.
Considering the integral, utilize Stokes' Theorem to determine an equivalent integral of the form:
In order to utilize Stokes' theorem, note its form
The curl of a vector functionFover an oriented surface年代is equivalent to the functionFitself integrated over the boundary curve,C, of年代.
Note that
From what we're told
Meaning that
From this we can derive our curl vectors
This allows us to set up our surface integral
Example Question #7 :年代urface Integrals
Let年代be a known surface with a boundary curve,C.
Considering the integral, utilize Stokes' Theorem to determine an equivalent integral of the form:
In order to utilize Stokes' theorem, note its form
The curl of a vector functionFover an oriented surface年代is equivalent to the functionFitself integrated over the boundary curve,C, of年代.
Note that
From what we're told
Meaning that
From this we can derive our curl vectors
This allows us to set up our surface integral
Example Question #8 :年代urface Integrals
Let年代be a known surface with a boundary curve,C.
Considering the integral, utilize Stokes' Theorem to determine an equivalent integral of the form:
In order to utilize Stokes' theorem, note its form
The curl of a vector functionFover an oriented surface年代is equivalent to the functionFitself integrated over the boundary curve,C, of年代.
Note that
From what we're told
Meaning that
From this we can derive our curl vectors
This allows us to set up our surface integral
Example Question #9 :年代urface Integrals
Let年代be a known surface with a boundary curve,C.
Considering the integral, utilize Stokes' Theorem to determine an equivalent integral of the form:
In order to utilize Stokes' theorem, note its form
The curl of a vector functionFover an oriented surface年代is equivalent to the functionFitself integrated over the boundary curve,C, of年代.
Note that
From what we're told
Meaning that
From this we can derive our curl vectors
This allows us to set up our surface integral
Example Question #10 :年代urface Integrals
Let年代be a known surface with a boundary curve,C.
Considering the integral, utilize Stokes' Theorem to determine an equivalent integral of the form:
In order to utilize Stokes' theorem, note its form
The curl of a vector functionFover an oriented surface年代is equivalent to the functionFitself integrated over the boundary curve,C, of年代.
Note that
From what we're told
Meaning that
From this we can derive our curl vectors
This allows us to set up our surface integral
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