Find the number b such that the line y = b divides the region bounded by the curves y = x^2 and y = 4 into two regions with equal area. Give your answer correct to 3 decimal places.

Question

agl202 · Answer

9x² = 25 .......... find the intersections 
x = ± 5/3 

A = 2 ∫ 25 - 9x² dx [0,5/3] ........ area bounded by y = 25 and y = 9x² 
= 500/9 

9x² = b .......... find the intersections 
x = √b/3 

250/9 = 2 ∫ b - 9x² dx [0,√b/3] .... half the area 
250/9 = 2bx - 6x^3 [0,√b/3] 
250/9 = 4/9 b^(3/2) 
b = 25/∛4 

Answer: b = 25/∛4 .... or approx. 15.74901312
Hope this helps u!!! =)

anonymous · Answer

thank u!!!!!!!!!!!!!! :)

agl202 · Answer

Anytime!

anonymous · Answer

can u plz help me with another one? :)