The area of the plane region bounded by the curves `x""+""2y^2=""0` and `x""+""3y^2=""1` is equal to (1) `5/3` (2) `1/3` (3) `2/3` (4) `4/3`

Options

A. `(4)/(3)` sq units
B. `(5)/(3)` sq unit
C. `(1)/(3)` sq unit
D. `(2)/(3)` sq unit

Explanation

To find the area of the plane region bounded by the curves \( x + 2y^2 = 0 \) and \( x + 3y^2 = 1 \), we will follow these steps:

### Step 1: Find the Points of Intersection
To find the points of intersection of the two curves, we set the equations equal to each other.

1. From the first curve:
\[
x = -2y^2
...