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
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7 concepts
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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.

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Area of a Surface of Revolution

If the curve is described by the function $y = f(x) (a≤x≤b)$, the area $A_y$ is given by the integral $A_x = 2\pi\int_a^bf(x)\sqrt{1+\left(f'(x)\right)^2} \, dx$ for revolution around the $x$-axis.

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Physics and Engineering: Fluid Pressure and Force

Pressure is given as $p = \frac{F}{A}$ or $p = \frac{dF_n}{dA}$, where $p$ is the pressure, $\mathbf{F}$ is the normal force, and $A$ is the area of the surface on contact.

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Physics and Engeineering: Center of Mass

For a continuous mass distribution, the position of center of mass is given as $\mathbf R = \frac 1M \int_V\rho(\mathbf{r}) \mathbf{r} dV$ .

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Applications to Economics and Biology

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

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Probability

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

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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.

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