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Find the centroid of the area bounded by the curves y=x³, x=0 and y=8 

 Jul 22, 2021
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Let,NavyArmyCCU

f(x)=x3 and g(x)=8

Given that,

x=0

In order to find second interval, we have to find the point of intersection of y=x3 and y=8

Hence, 8=x3 ∴x=2

hence the interval is, [0,2]

Area = ∫ab​[f(x)−g(x)]dx where, f(x)>g(x)

In the given example, g(x)>f(x)

∴ Area = ∫02​[8−x3]dx

∴A=[8x−4x4​]02​

∴A=[16−4]−[0−0]

∴A=12 sq.units

 Jul 22, 2021

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