Calculus
Textbooks
Boundless Calculus
Inverse Functions and Advanced Integration
Calculus Textbooks Boundless Calculus Inverse Functions and Advanced Integration
Calculus Textbooks Boundless Calculus
Calculus Textbooks
Calculus

Section 3

Further Applications of Integration

Book Version 1
By Boundless
Boundless Calculus
Calculus
by Boundless
View the full table of contents
7 concepts
Thumbnail
Arc Length and Surface Area

Infinitesimal calculus provides us general formulas for the arc length of a curve and the surface area of a solid.

Thumbnail
Area of a Surface of Revolution

If the curve is described by the function $y = f(x) (a≤x≤b)$, the area AyA_yA​y​​ is given by the integral Ax=2π∫abf(x)1+(f′(x))2dxA_x = 2\pi\int_a^bf(x)\sqrt{1+\left(f'(x)\right)^2} \, dxA​x​​=2π∫​a​b​​f(x)√​1+(f​′​​(x))​2​​​​​dx for revolution around the xxx-axis.

Thumbnail
Physics and Engineering: Fluid Pressure and Force

Pressure is given as p=FAp = \frac{F}{A}p=​A​​F​​ or p=dFndAp = \frac{dF_n}{dA}p=​dA​​dF​n​​​​, where ppp is the pressure, F\mathbf{F}F is the normal force, and AAA is the area of the surface on contact.

Thumbnail
Physics and Engeineering: Center of Mass

For a continuous mass distribution, the position of center of mass is given as R=1M∫Vρ(r)rdV\mathbf R = \frac 1M \int_V\rho(\mathbf{r}) \mathbf{r} dVR=​M​​1​​∫​V​​ρ(r)rdV .

Thumbnail
Applications to Economics and Biology

Calculus has broad applications in diverse fields of science; examples of integration can be found in economics and biology.

Thumbnail
Probability

Probability density function describes the relative likelihood, or probability, that a given variable will take on a value.

Thumbnail
Taylor Polynomials

A Taylor series is a representation of a function as an infinite sum of terms calculated from the values of the function's derivatives.

Subjects
  • Accounting
  • Algebra
  • Art History
  • Biology
  • Business
  • Calculus
  • Chemistry
  • Communications
  • Economics
  • Finance
  • Management
  • Marketing
  • Microbiology
  • Physics
  • Physiology
  • Political Science
  • Psychology
  • Sociology
  • Statistics
  • U.S. History
  • World History
  • Writing

Except where noted, content and user contributions on this site are licensed under CC BY-SA 4.0 with attribution required.