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XJellieBX

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## Homework Statement

The region between y=cos x and the x-axis for x [tex]\in[/tex] [0, [tex]\pi[/tex]/2] is divided into two subregions of equal area by a line y=c. Find c.

**2. The attempt at a solution**

First I drew a graph of the region bounded between the function and the x-axis in [0, [tex]\pi[/tex]/2]. Next I found the total area of the region:

[tex]A_{1,2}[/tex] = [tex]\int^{\pi/2}_{0}[/tex] cos x dx = sin x |[tex]^{\pi/2}_{0}[/tex] = 1

Dividing the total area by 2, gives the area of each portion divided by y=c.

[tex]A_{1}[/tex] = 1/2 = [tex]\int^{c}_{0}[/tex] [tex]cos^{-1}[/tex] (y) dy = y[tex]cos^{-1}[/tex] (y) - [tex]\sqrt{1-y^{2}}[/tex] [tex]|^{c}_{0}[/tex]

= c (cos[tex]^{-1}[/tex] (c)) - [tex]\sqrt{1-c^{2}}[/tex] + 1

--> c ([tex]cos^{-1}[/tex] (c)) - [tex]\sqrt{1-c^{2}}[/tex] = -1/2

I'm not sure how to solve for c from the equation above. Any input will be appreciated.

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