Find the centroid of the region in the first quadrant

vetrila10 2021-12-01 Answered
Find the centroid of the region in the first quadrant bounded by the given curves.
y=x3,x=y3
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Expert Answer

Michele Grimsley
Answered 2021-12-02 Author has 19 answers
Step 1
Given
y=x3,x=y3
Step 2
f(x)=x3andg(x)=y=x13
My=01x[f(x)g(x)]dx
=01x[x3x13]dx
=01[x4x43]dx
=15[x5]0137[x73]01
=1537=835
Mx=1201[(x)6(x)23]dx
=12[17[x]735[x]53]01
=12[1735]
=835
M=01[f(x)g(x)]dx
=01[(x)3(x)13]dx
=14[x4]0134[x43]01
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