What is the area under a sine wave from 0 to pi?. Hint: do not use the digital form of pi, use pi = 180 degrees.

Question

First Clue: this is not related to the area of a circle (pi r squared). What's interesting about pi, is that it comes in 2 forms: digital (3.14159....) and degrees of a 1/2 circle (180 degrees). And a sine wave is an incredibly beautiful curve found everywhere in nature.

Once you get the answer, memorize it and how you arrived at it. And it will serve as a reference for problem solving in wave mechanics.

Remember, according to the De Broglie Wave Equation, everything in the entire Cosmos travels as both a wave and a particle. And sine waves, or approximations to sine waves, are the standard form of travel representing everything from light waves, sound waves, to waves on an ocean.

The study of wave mechanics will then lead you to the understanding of Fourier Analysis/Transformation, noise cancellation head phones, and unlimited adventures in science and math.

Moral of the story: Sine Waves rule! And to figure out how powerful they are you must know how to integrate the area/volume.
Second Clue: "integrate".

Answer 1

Area under any curve within a range is just the integral of the function describing the curve limited by the mentioned range.

Comments

Excellent!  An accurate and concise answer + a diagram. It's like having a math tutor
right in your own living room.  Wish I had this website when I was a student.

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Thank you :)