Find the centroid of the region bounded by the given curves. $$y = 2 x ^ { 3 } , 2 x + y = 4 , x = 0$$
A) $\frac { 92 } { 105 } , \frac { 9 } { 75 }$
B) $\frac { 58 } { 75 } , \frac { 370 } { 105 }$
C) $\frac { 28 } { 75 } , \frac { 184 } { 105 }$
D) $\frac { 370 } { 75 } , \frac { 58 } { 105 }$
E) None of these

Question

Quizplus · Accepted Answer

The centroid of the region can be found by integrating the given curves and using the formulas for the centroid of a region bounded by curves. After solving, the centroid is $\frac { 28 } { 75 } , \frac { 184 } { 105 }$.

Find the Centroid of the Region Bounded by the Given y=2x3,2x+y=4,x=0y = 2 x ^ { 3 } , 2 x + y = 4 , x = 0y=2x3,2x+y=4,x=0

Find the Centroid of the Region Bounded by the Given $y = 2 x ^ { 3 } , 2 x + y = 4 , x = 0$