Tabatabaian T. 100 Integrals: Solutions with Engineering Applications

Boston: Mercury Learning and Information, 2023. — 216 p. — ISBN 1683929659.This monograph contains a collection of integrals, some more challenging than others, with their worked-out solutions as indefinite integrals. The integrals were randomly selected, modified, or designed with the condition of having closed forms solutions with common functions. This list is meant for helping readers in practicing and getting hints for working out solutions to similar integrals that they might encounter. Readers might want to add their own favorite integrals to this list. We also present the application of some integrals in engineering related topics. For example, nonuniform loading, hydrostatic force, moment of inertia, polar moment of inertia, etc. We introduce an up-to-date online software tool, WolframAlpha, that can be used for comparing our answers for the integrals listed. However, readers may want to update to WolframAlpha Pro for recovering some of the integrals' step-by-step solutions. In addition, similar CAS (computer algebra system) tools like Maple, Mathematica, or Mathcad may also be employed.
Features:
Presents the application of some integrals in engineering related topics, e.g., nonuniform loading, hydrostatic force, moment of inertia, polar moment of inertia, etc.
Introduces the up-to-date, online software tool, WolframAlpha, that can be used for comparing answers for the integrals listed.Preface
About the Author
List of selected integrals with their step-by-step solutions
Integrals 1-100
Examples applied in engineering
Semi-Circle Shapes
Circular Segment Shapes
Semi-Ellipse Shapes
Two-Degree Polynomial Shape-Quadratic
Three-Degree Polynomial Shape-Cubic
n-Degree Polynomial Shape-Spandrel
Sinusoidal Shapes
Triangular Shapes
Rectangular Shapes
Complex Shapes
A Cantilever Beam with Cubic Load Distribution
A Cantilever Beam with Quarter-Ellipse. Load Distribution
A Cantilever Beam with Inverse Cosine. Load Distribution
A Cantilever Beam with Parabolic. Load Distribution
A Cantilever Beam with Circular Segment. Cross-Section and Quarter-Ellipse
Load Distribution
Probability Density Functions (PDF)
ReferencesTrue PDF