Change of Variables - Multivariable Calculus
Card 1 of 12
Convert the following into spherical coordinates.
Convert the following into spherical coordinates.
Tap to reveal answer
In order to convert to spherical coordinates , we need to remember the conversion equations.
Now lets apply this to our problem.
In order to convert to spherical coordinates , we need to remember the conversion equations.
Now lets apply this to our problem.
← Didn't Know|Knew It →
Evaluate 
, where 
is the trapezoidal region with vertices given by 
, 
, 
, and 
,
using the transformation 
, and 
.
Evaluate
using the transformation
Tap to reveal answer
The first thing we have to do is figure out the general equations for the lines that create the trapezoid.
Now we have the general equations for out trapezoid, now we need to plug in our transformations into these equations.
So our region is a rectangle given by 
, 
Next we need to calculate the Jacobian.
Now we can put the integral together.
The first thing we have to do is figure out the general equations for the lines that create the trapezoid.
Now we have the general equations for out trapezoid, now we need to plug in our transformations into these equations.
So our region is a rectangle given by
Next we need to calculate the Jacobian.
Now we can put the integral together.
← Didn't Know|Knew It →
Convert the following into spherical coordinates.
Convert the following into spherical coordinates.
Tap to reveal answer
In order to convert to spherical coordinates , we need to remember the conversion equations.
Now lets apply this to our problem.
In order to convert to spherical coordinates , we need to remember the conversion equations.
Now lets apply this to our problem.
← Didn't Know|Knew It →
Convert the following into spherical coordinates.
Convert the following into spherical coordinates.
Tap to reveal answer
In order to convert to spherical coordinates , we need to remember the conversion equations.
Now lets apply this to our problem.
In order to convert to spherical coordinates , we need to remember the conversion equations.
Now lets apply this to our problem.
← Didn't Know|Knew It →
Evaluate , where is the trapezoidal region with vertices given by , , , and ,
using the transformation , and .
Evaluate
using the transformation
Tap to reveal answer
The first thing we have to do is figure out the general equations for the lines that create the trapezoid.
Now we have the general equations for out trapezoid, now we need to plug in our transformations into these equations.
So our region is a rectangle given by ,
Next we need to calculate the Jacobian.
Now we can put the integral together.
The first thing we have to do is figure out the general equations for the lines that create the trapezoid.
Now we have the general equations for out trapezoid, now we need to plug in our transformations into these equations.
So our region is a rectangle given by
Next we need to calculate the Jacobian.
Now we can put the integral together.
← Didn't Know|Knew It →
Convert the following into spherical coordinates.
Convert the following into spherical coordinates.
Tap to reveal answer
In order to convert to spherical coordinates , we need to remember the conversion equations.
Now lets apply this to our problem.
In order to convert to spherical coordinates , we need to remember the conversion equations.
Now lets apply this to our problem.
← Didn't Know|Knew It →
Convert the following into spherical coordinates.
Convert the following into spherical coordinates.
Tap to reveal answer
In order to convert to spherical coordinates , we need to remember the conversion equations.
Now lets apply this to our problem.
In order to convert to spherical coordinates , we need to remember the conversion equations.
Now lets apply this to our problem.
← Didn't Know|Knew It →
Evaluate , where is the trapezoidal region with vertices given by , , , and ,
using the transformation , and .
Evaluate
using the transformation
Tap to reveal answer
The first thing we have to do is figure out the general equations for the lines that create the trapezoid.
Now we have the general equations for out trapezoid, now we need to plug in our transformations into these equations.
So our region is a rectangle given by ,
Next we need to calculate the Jacobian.
Now we can put the integral together.
The first thing we have to do is figure out the general equations for the lines that create the trapezoid.
Now we have the general equations for out trapezoid, now we need to plug in our transformations into these equations.
So our region is a rectangle given by
Next we need to calculate the Jacobian.
Now we can put the integral together.
← Didn't Know|Knew It →
Convert the following into spherical coordinates.
Convert the following into spherical coordinates.
Tap to reveal answer
In order to convert to spherical coordinates , we need to remember the conversion equations.
Now lets apply this to our problem.
In order to convert to spherical coordinates , we need to remember the conversion equations.
Now lets apply this to our problem.
← Didn't Know|Knew It →
Convert the following into spherical coordinates.
Convert the following into spherical coordinates.
Tap to reveal answer
In order to convert to spherical coordinates , we need to remember the conversion equations.
Now lets apply this to our problem.
In order to convert to spherical coordinates , we need to remember the conversion equations.
Now lets apply this to our problem.
← Didn't Know|Knew It →
Evaluate , where is the trapezoidal region with vertices given by , , , and ,
using the transformation , and .
Evaluate
using the transformation
Tap to reveal answer
The first thing we have to do is figure out the general equations for the lines that create the trapezoid.
Now we have the general equations for out trapezoid, now we need to plug in our transformations into these equations.
So our region is a rectangle given by ,
Next we need to calculate the Jacobian.
Now we can put the integral together.
The first thing we have to do is figure out the general equations for the lines that create the trapezoid.
Now we have the general equations for out trapezoid, now we need to plug in our transformations into these equations.
So our region is a rectangle given by
Next we need to calculate the Jacobian.
Now we can put the integral together.
← Didn't Know|Knew It →
Convert the following into spherical coordinates.
Convert the following into spherical coordinates.
Tap to reveal answer
In order to convert to spherical coordinates , we need to remember the conversion equations.
Now lets apply this to our problem.
In order to convert to spherical coordinates , we need to remember the conversion equations.
Now lets apply this to our problem.
← Didn't Know|Knew It →