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Area Under the curve

Calculus
Tutor: None Selected Time limit: 1 Day

How to find area under the curve. Sin(x) from 0 to 2Pi. Explain in details

Mar 16th, 2015

√( 1 + (dy/dx)^2 )
√( 1 + (cos(x))^2 )
√( 1 + cos^2(x) )


∫ √( 1 + cos^2(x) ) dx ≈ 7.64
0

Area:


∫ (sin(x) + 2 - 0) dx
0


∫ sin(x) + 2 dx 0
2π - cos(x) + 2x ] 0

- ( cos(2π) - cos(0) ) + 2 * (2π - 0)
- ( 1 - 1 ) + 2 * (2π)
4π 

That is the length of the curve, but that integral has no closed form, however, it does result in a real number, so technically it's a real number and thus a length.

Mar 16th, 2015

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