Solve the problem.
-Find the coordinates of the centroid of the area bounded by $y = x ^ { 2 }$ and $y = 3$
A) $\left( 0 , \frac { 18 } { 5 } \right)$
B) $( 0,5 )$
C) $\left( 0 , \frac { 9 } { 5 } \right)$
D) $\left( 0 , \frac { 27 } { 5 } \right)$

Question

Quizplus · Accepted Answer

The area bounded by the curves is given by 
$$\int_{0}^{\sqrt{3}} \left( 3 - x^2 \right) dx$$

Using the formula for the centroid of the region, we get
$$\left( \frac{1}{A}\int_{0}^{\sqrt{3}} \frac{x\left(3-x^2\right)}{2} dx, \frac{1}{A} \int_{0}^{\sqrt{3}} \frac{\left(3-x^2\right)}{2} dx \right)$$
where $A$ is the area of the region.
Evaluating the integrals, we get the centroid as $\left( 0 , \frac {9}{5} \right)$. Therefore, the best choice is C.

Solve the Problem y=x2y = x ^ { 2 }y=x2 And y=3y = 3y=3

Solve the Problem $y = x ^ { 2 }$ And $y = 3$