area of a circle segment

**rmpatel5** · September 12th 2008, 01:58 PM

is this suffice to calculate the area of a circle segment? Prove why or why not?

**Jhevon** · September 12th 2008, 02:22 PM

Originally Posted by rmpatel5

is this suffice to calculate the area of a circle segment? Prove why or why not?

this integral gives the area "under" a straight line $ax + b$ between the limits $x_0$ and $x_1$

**Soroban** · September 12th 2008, 02:23 PM

Hello, rmpatel5!

Who asked this question ??
It has nothing to do with a circle . . .

$\int^{x_1}_{x_o}(ax + b)\,dx$

Is this suffice to calculate the area of a circle segment? . . . . certainly not!

Code:

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          *     |     *
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       *        |     |::*
                |     |:::
      *         |     |:::*
  - - * - - - - + - -a+:::*r- -
      *         |     |:::*
                |     |:::
       *        |     |::*
        *       |     |:*
          *     |     *
              * * *
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We have: . $x^2+y^2 \:=\:r^2 \quad\Rightarrow\quad y \:=\:\sqrt{r^2 - x^2}$ . (the upper semicircle)

The area is: . $A \;=\;2 \times \int^r_a \left(r^2 - x^2\right)^{\frac{1}{2}}\,dx$

**rmpatel5** · September 12th 2008, 02:53 PM

Originally Posted by Soroban

Hello, rmpatel5!

Who asked this question ??
It has nothing to do with a circle . . .

Code:

                |
              * * *
          *     |     *
        *       |     |:*
       *        |     |::*
                |     |:::
      *         |     |:::*
  - - * - - - - + - -a+:::*r- -
      *         |     |:::*
                |     |:::
       *        |     |::*
        *       |     |:*
          *     |     *
              * * *
                |

We have: . $x^2+y^2 \:=\:r^2 \quad\Rightarrow\quad y \:=\:\sqrt{r^2 - x^2}$ . (the upper semicircle)

The area is: . $A \;=\;2 \times \int^r_a \left(r^2 - x^2\right)^{\frac{1}{2}}\,dx$

hahah..my history of calculus teacher. He is kind of a nut. Also in your integral arnt u missing the part where u minus the integral of the line segment with the area of the circle??

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