Every problem in the chapter beside the book’s answer, a chapter at a time as you scroll.
Chapter 12: Practice: Triple Integrals and Surface Integrals in 3-Space
44 problems · 119 figures1 §12.1 source ↗
Answer
2 §12.1 source ↗
Answer
1 §12.1 source ↗
Answer
2 §12.1 source ↗
Answer
Practice with Triple Integrals §12.2 source ↗
Answer
1 §12.3 source ↗
Answer
2 §12.3 source ↗
Answer
3 §12.3 source ↗
Answer
1 §12.4 source ↗
Answer
Jacobian for Spherical Coordinates §12.4 source ↗
Answer
1 §12.4 source ↗
Answer
2 §12.4 source ↗
Answer
Applications of Spherical Coordinates §12.5 source ↗
Answer
Vector Fields in Space §12.6 source ↗
Answer
1 §12.7 source ↗
Answer
2 §12.7 source ↗
Answer
1 §12.8 source ↗
Answer
2 §12.8 source ↗
Answer
3 §12.8 source ↗
Answer
1 §12.9 source ↗
Answer
2 §12.9 source ↗
Answer
Flux Through a Paraboloid §12.10 source ↗
Answer
General Formula for n dS §12.10 source ↗
Answer
Divergence Theorem §12.11 source ↗
Answer
1 §12.12 source ↗
Answer
2 §12.12 source ↗
Answer
1 §12.13 source ↗
Answer
2 §12.13 source ↗
Answer
3 §12.13 source ↗
Answer
4 §12.13 source ↗
Answer
1 §12.14 source ↗
Answer
2 §12.14 source ↗
Answer
Gradient Fields and Potential Functions §12.15 source ↗
Answer
1 §12.16 source ↗
Answer
2 §12.16 source ↗
Answer
1 §12.16 source ↗
Answer
2 §12.16 source ↗
Answer
1 §12.17 source ↗
Answer
2 §12.17 source ↗
Answer
Extended Stokes’ Theorem §12.18 source ↗
Answer
Extended Stokes’ Theorem §12.18 source ↗
Answer
1 §12.19 source ↗
Answer
2 §12.19 source ↗
Answer
Surface Independence §12.20 source ↗
Answer
End of the book.
Exercises and answers are adapted from 18.02SC Multivariable Calculus by Prof. Denis Auroux, which is free to read and download, and are used under the CC BY-NC-SA 4.0 licence. They are taken from the course’s problem and solution PDFs, cropped as printed, and set for the web, so they may differ slightly from the printed page. This adaptation is released under the same licence and is neither affiliated with nor endorsed by Auroux or MIT OpenCourseWare.