The SC strip
Have you ever thought of the sine and cosine function like this?
I have constructed a bi-coloured strip as shown above. I call it the strip. One side of the strip is coloured blue while the other side is coloured red.
So, here's the problem: Find the surface area of the strip bounded between .
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5 solutions
Consider the area of the strip between [ 0 , π ] .
The areas are listed above. First calculate the area of the blue surface. Note that you have to add the surface with area 2 π − 2 twice as it appears in the front as well as the back (can't be seen). You will get π after adding all these areas.
But don't stop here. The other (red) side of the strip will have the same area. So, the net area becomes 2 π .
Thus, for [ 0 , k π ] , the answer becomes 2 k π as it is periodic with period π .