4. $[-12$ Points $]$ DETAILS SCALC9 5.1.010. MY NOTES ASK YOUR TEACHER Set up an integral representing the area $A$ of the region enclosed by the given curves. \[ x=y^{4}, x=2-y^{2} \] \[ A=\int_{-1}(\square) d y \] Need Help? Read It Submit Answer

Step 1 ：First, we need to find the intersection points of the two curves $x=y^{4}$ and $x=2-y^{2}$. The intersection points are -1 and 1. The other two points are imaginary and are not considered in this context.

Step 2 ：Next, we set up the integral from -1 to 1 (the intersection points). The integrand will be the absolute difference between the two functions. We need to determine which function is greater in the interval from -1 to 1.

Step 3 ：Finally, we calculate the integral to find the area of the region enclosed by the curves. The area is \(\frac{44}{15}\).

Step 4 ：Final Answer: The area of the region enclosed by the curves $x=y^{4}$ and $x=2-y^{2}$ is \(\boxed{\frac{44}{15}}\).