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Double and triple integrals and change of variables · GRE Mathematics Subject Test · Courselo

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Calculus III: multivariable and vector calculus

Double and triple integrals and change of variables

Calculus III: multivariable and vector calculus · Lesson 4 of 5

Lesson 4 of 5

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Unit 3

Calculus III: multivariable and vector calculus

5 lessons · 5 h 55 min of study

Vectors, lines, planes and curves in space1 h of study
Partial derivatives, gradients and tangent planes1 h 15 min of study
Optimization in several variables and Lagrange multipliers1 h of study
Double and triple integrals and change of variablesReading · 0%
Line and surface integrals and the theorems of vector calculus1 h 20 min of study

This unit is ≈15% of the GRE Math, across 5 lessons. Full syllabus

Lesson 4 of 5 · Calculus III: multivariable and vector calculus

Double and triple integrals and change of variables

3 quick checks≈4% of the testCore: Core: tested on most papers

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By the end you’ll be able to

Evaluate double and triple integrals over general regions, choosing a convenient order of integration
Reverse the order of integration to evaluate iterated integrals that cannot be done in the given order
Change variables to polar, cylindrical and spherical coordinates, and use the Jacobian determinant for general substitutions

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Adaptive questions on double and triple integrals and change of variables.

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Apply multiple integrals to area, volume, mass, average value and probability over regions

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