Find the centroid of the region bounded by the given curves. y=x³, x + y=10, y=0.

Solution:

Given curves y = x³ ----->(1)

x + y=10 ---->(2)

y = 0 ------>(3)

Solving (2) and (3) y=0, x+y=10 we get (10,0)

Solving (1) and (3) y=0, y=x³, we get (0,0)

Solving (1) and (2) x+y=10, y=x³, we get x=2

Ignore the complex root in the above step

Centroid of (2,8), (0,0) and (10,0) is ((x\(_1\)+x\(_2\)+x\(_3\))/3, (y\(_1\)+ y\(_2\)+y\(_3\))/3)

={(2+0+10)/3, (8+0+0)/3}

= (12/3, 8/3}

= (4,8/3)

Find the centroid of the region bounded by the given curves. y=x^³, x + y=10, y=0.

Summary:

The centroid of the region is bounded by the given curves. y=x³, x + y=10, y=0 is (4,8/3).