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The region bounded by the x-axis?

The region bounded by the x-axis and the part of the graph of y=cos x between x=-pi/2 and x=pi/2 is separated into two regions by the line x=k. If the area of the region for -pi/2≤x≤k is three times the area of the region for k≤x≤pi/2, what's k?
 
Answer: pi/6
 
 
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1 Answer

(-pi/2)(pi/2) cos(x)dx = 2
 
(-pi/2)cos(x)dx + ∫k(pi/2) = 2
 
(-pi/2)k cos(x)dx =  (1/2) = 3*∫k(pi/2)cos(x)dx = 3*(1/2)
 
sin(k) - sin(-pi/2) = 3sin(pi/2) - 3sin(k)
 
sin(k) = -3[sin(k)]
 
sin(k) = -3[sin(k)]
 
sin(k) + 3[sin(k)] = 2
 
4[sin(k)] = 2
 
sin(k) = (1/2)
 
k = (pi/6) radians or 30º
 
 
 
 
 
 

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