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Formulas

Math

Showing formulas of Math

Showing 12 of 36 formulas Page 2 of 2

Volume of a Cylinder

Math → Geometry → 3d Shapes → Volume
$$V = \pi r^2 h$$
Capacity of a solid with two parallel circular bases.
📖 Math 📚 3d Shapes

Limit Definition of Derivative

Math → Calculus → Differentiation → Fundamentals
$$f'(x) = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h}$$
The exact rate of change at a specific point.
📖 Math 📚 Differentiation

Integration of Secant Squared

Math → Calculus → Integrals → Trigonometric Integration
$$\int \sec^2 x \, dx = \tan x + C$$
The standard integral for the square of the secant function.
📖 Math 📚 Integrals

Area of a Triangle (Heron's Formula)

Math → Geometry → Triangles → Area
$$A = \sqrt{s(s-a)(s-b)(s-c)}$$
Calculates the area of a triangle when only the lengths of the three sides are known.
📖 Math 📚 Triangles

Slope-Intercept Form

Math → Algebra → Linear Equations → Graphing
$$y = mx + c$$
A standard way to represent a straight line on a Cartesian plane.
📖 Math 📚 Linear Equations

Integration of $1/\sqrt{a^2 - x^2}$

Math → Calculus → Integrals → Inverse Trig Integrals
$$\int \frac{dx}{\sqrt{a^2 - x^2}} = \sin^{-1}\left(\frac{x}{a}\right) + C$$
Standard integral result involving inverse sine.
📖 Math 📚 Integrals

Integration of Logarithm

Math → Calculus → Integrals → Integration Techniques
$$\int \ln x \, dx = x \ln x - x + C$$
The antiderivative of the natural logarithm function.
📖 Math 📚 Integrals

Integration of $1/(x^2 + a^2)$

Math → Calculus → Integrals → Integration Formulas
$$\int \frac{dx}{x^2 + a^2} = \frac{1}{a} \tan^{-1}\left(\frac{x}{a}\right) + C$$
Standard integral leading to the inverse tangent function.
📖 Math 📚 Integrals

Area of a Regular Polygon

Math → Geometry → Polygons → Area
$$A = \frac{1}{2} n s a$$
Calculates the area of any regular polygon given its number of sides, side length, and apothem.
📖 Math 📚 Polygons

Integration of $a^x$

Math → Calculus → Integrals → Exponential Integration
$$\int a^x \, dx = \frac{a^x}{\ln a} + C$$
The general integral for exponential functions where the base is any positive constant.
📖 Math 📚 Integrals

Volume of a Pyramid

Math → Geometry → 3d Shapes → Volume
$$V = \frac{1}{3}Bh$$
The capacity of a pyramid with any polygon base.
📖 Math 📚 3d Shapes

Midpoint Formula (3D)

Math → Geometry → Coordinate Geometry → Analytical Geometry
$$M = \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}, \frac{z_1+z_2}{2}\right)$$
Finds the coordinates of the exact center point between two endpoints in 3D space.
📖 Math 📚 Coordinate Geometry
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