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- https://math.libretexts.org/Courses/City_College_of_San_Francisco/CCSF_Calculus/15%3A_Multiple_Integration/15.08%3A_Change_of_Variables_in_Multiple_IntegralsWhen solving integration problems, we make appropriate substitutions to obtain an integral that becomes much simpler than the original integral. We also used this idea when we transformed double inte...When solving integration problems, we make appropriate substitutions to obtain an integral that becomes much simpler than the original integral. We also used this idea when we transformed double integrals in rectangular coordinates to polar coordinates and transformed triple integrals in rectangular coordinates to cylindrical or spherical coordinates to make the computations simpler.
- https://math.libretexts.org/Bookshelves/Calculus/Calculus_(OpenStax)/15%3A_Multiple_Integration/15.07%3A_Change_of_Variables_in_Multiple_IntegralsWhen solving integration problems, we make appropriate substitutions to obtain an integral that becomes much simpler than the original integral. We also used this idea when we transformed double inte...When solving integration problems, we make appropriate substitutions to obtain an integral that becomes much simpler than the original integral. We also used this idea when we transformed double integrals in rectangular coordinates to polar coordinates and transformed triple integrals in rectangular coordinates to cylindrical or spherical coordinates to make the computations simpler.
- https://math.libretexts.org/Bookshelves/Calculus/Vector_Calculus_(Corral)/03%3A_Multiple_Integrals/3.05%3A_Change_of_Variables_in_Multiple_IntegralsGiven the difficulty of evaluating multiple integrals, the reader may be wondering if it is possible to simplify those integrals using a suitable substitution for the variables. The answer is yes, tho...Given the difficulty of evaluating multiple integrals, the reader may be wondering if it is possible to simplify those integrals using a suitable substitution for the variables. The answer is yes, though it is a bit more complicated than the substitution method which you learned in single-variable calculus.
- https://math.libretexts.org/Courses/De_Anza_College/Calculus_IV%3A_Multivariable_Calculus/02%3A_Multiple_Integration/2.08%3A_Change_of_Variables_in_Multiple_IntegralsWhen solving integration problems, we make appropriate substitutions to obtain an integral that becomes much simpler than the original integral. We also used this idea when we transformed double inte...When solving integration problems, we make appropriate substitutions to obtain an integral that becomes much simpler than the original integral. We also used this idea when we transformed double integrals in rectangular coordinates to polar coordinates and transformed triple integrals in rectangular coordinates to cylindrical or spherical coordinates to make the computations simpler.
- https://math.libretexts.org/Under_Construction/Purgatory/MAT-004A_-_Multivariable_Calculus_(Reed)/04%3A_Multiple_Integration/4.07%3A_Change_of_Variables_in_Multiple_IntegralsWhen solving integration problems, we make appropriate substitutions to obtain an integral that becomes much simpler than the original integral. We also used this idea when we transformed double inte...When solving integration problems, we make appropriate substitutions to obtain an integral that becomes much simpler than the original integral. We also used this idea when we transformed double integrals in rectangular coordinates to polar coordinates and transformed triple integrals in rectangular coordinates to cylindrical or spherical coordinates to make the computations simpler.
- https://math.libretexts.org/Courses/SUNY_Geneseo/Math_223_Calculus_3/04%3A_Multiple_Integration/4.07%3A_Change_of_Variables_in_Multiple_IntegralsWhen solving integration problems, we make appropriate substitutions to obtain an integral that becomes much simpler than the original integral. We also used this idea when we transformed double inte...When solving integration problems, we make appropriate substitutions to obtain an integral that becomes much simpler than the original integral. We also used this idea when we transformed double integrals in rectangular coordinates to polar coordinates and transformed triple integrals in rectangular coordinates to cylindrical or spherical coordinates to make the computations simpler.
- https://math.libretexts.org/Bookshelves/Calculus/Supplemental_Modules_(Calculus)/Vector_Calculus/3%3A_Multiple_Integrals/3.9%3A_Substitutions_in_Multiple_IntegralsThis section discusses the translation of a graph from the xy Cartesian plane to the uv Cartesian plane and defines the Jacobian. The Jacobian measures how much the volume at a certain point chang...This section discusses the translation of a graph from the xy Cartesian plane to the uv Cartesian plane and defines the Jacobian. The Jacobian measures how much the volume at a certain point changes when being transformed from one coordinate system to another.
- https://math.libretexts.org/Bookshelves/Calculus/Supplemental_Modules_(Calculus)/Vector_Calculus/3%3A_Multiple_Integrals/3.8%3A_JacobiansThe goal for this section is to be able to find the "extra factor" for a more general transformation. We call this "extra factor" the Jacobian of the transformation. We can find it by taking the deter...The goal for this section is to be able to find the "extra factor" for a more general transformation. We call this "extra factor" the Jacobian of the transformation. We can find it by taking the determinant of the two by two matrix of partial derivatives.
- https://math.libretexts.org/Courses/University_of_Maryland/MATH_241/04%3A_Multiple_Integration/4.08%3A_Change_of_Variables_in_Multiple_IntegralsWhen solving integration problems, we make appropriate substitutions to obtain an integral that becomes much simpler than the original integral. We also used this idea when we transformed double inte...When solving integration problems, we make appropriate substitutions to obtain an integral that becomes much simpler than the original integral. We also used this idea when we transformed double integrals in rectangular coordinates to polar coordinates and transformed triple integrals in rectangular coordinates to cylindrical or spherical coordinates to make the computations simpler.
- https://math.libretexts.org/Courses/Mission_College/Math_4A%3A_Multivariable_Calculus_v2_(Reed)/15%3A_Multiple_Integration/15.07%3A_Change_of_Variables_in_Multiple_IntegralsWhen solving integration problems, we make appropriate substitutions to obtain an integral that becomes much simpler than the original integral. We also used this idea when we transformed double inte...When solving integration problems, we make appropriate substitutions to obtain an integral that becomes much simpler than the original integral. We also used this idea when we transformed double integrals in rectangular coordinates to polar coordinates and transformed triple integrals in rectangular coordinates to cylindrical or spherical coordinates to make the computations simpler.
- https://math.libretexts.org/Courses/Mission_College/Math_4A%3A_Multivariable_Calculus_(Kravets)/04%3A_Multiple_Integration/4.07%3A_Change_of_Variables_in_Multiple_IntegralsWhen solving integration problems, we make appropriate substitutions to obtain an integral that becomes much simpler than the original integral. We also used this idea when we transformed double inte...When solving integration problems, we make appropriate substitutions to obtain an integral that becomes much simpler than the original integral. We also used this idea when we transformed double integrals in rectangular coordinates to polar coordinates and transformed triple integrals in rectangular coordinates to cylindrical or spherical coordinates to make the computations simpler.
