Equation of the circle is x^2 + y^2 = r^2

and the sector's angle = x

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- Jan 1st 2010, 01:06 PMAerospank[SOLVED] How to find using integration, the area of a circular sector with an angle,x
Equation of the circle is x^2 + y^2 = r^2

and the sector's angle = x - Jan 1st 2010, 02:19 PMskeeter
- Jan 1st 2010, 07:53 PMAerospank
- Jan 2nd 2010, 04:36 AMHallsofIvy
That

**is**derived from the equation of the circle! But if you want to do it in the**hard**way, using Cartesian coordinates, you can without loss of generality, assume one edge of the sector lies on x axis, from x= 0 to x= r. The other then lies on the line from x=0 to . Part of the area, then, is given by which is easy since r and are constants. But then you have to find the area of the portion under the circular arc, . That is . The total area of the sector is the sum of those integrals:

.

I think using polar coordinates is a much better idea. Of course, as a check, since a central angle of cuts of the entire circle, its area is that same fraction of the entire area of the circle, .