Khan Academy: Calculus: Euler's Formula and Euler's Identity

This video [4:48] shows how to determine the integral of an unusual function using geometry to find the area under the curve. Also shows how to find the derivative of a function which contains an integral by using the Fundamental Theorem...

Video lesson explaining why the antiderivative is the area under a curve. Provides an introduction to the fundamental theorem of calculus. [9:46]

Explains how to derive the quadratic formula by completing the square on the standard form of a quadratic equation. [7:34]

Demonstrates how to find the area of a triangle using Heron's formula. Practice problems available. [4:43]

Demonstrates how to solve a quadratic equation that begins in the form ax^2 + bx = c using the quadratic formula. [6:40]

Demonstrates how to use the quadratic formula to solve a quadratic equation with a negative leading coefficient. [5:34]

This video demonstrates how to find the distance between any two points on a the coordinate plane. It shows how the distance formula was derived using the Pythagorean theorem. Practice problems avaialble. This video is also found in the...

Video continues a discussion about the relationship between the polynomial approximations for the sine, cosine and e^x functions from Maclaurin series and uses those to derive Euler's formula and Euler's identity. [10:18]

Video shows how to use integrals to write a formula for the perimeter of an area bounded on one side by a function. Includes showing how to derive the arc length formula. [5:41]

Video shows how to derive the arc length formula and how to use it to determine the total distance a particle traveled during a given time interval. [8:34]