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DETAILS SCALC9 5.1.010.
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Set up an integral representing the area $A$ of the region enclosed by the given curves.
\[
\begin{array}{l}
x=y^{4}, x=2-y^{2} \\
A=\int_{-1}(\square) d y \\
\text { Need Help? Read It }
\end{array}
\]
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Answer

Calculate the integral to get the final answer: $\boxed{\frac{44}{15}}$.

Steps

Step 1 ：Solve the equations $x=y^4$ and $x=2-y^2$ for $y$ to get the functions to integrate.

Step 2 ：Subtract the smaller function from the larger one to get the integrand for the integral: $-y^4 - y^2 + 2$.

Step 3 ：Set up the integral with the correct limits of integration and the correct integrand.

Step 4 ：Calculate the integral to get the final answer: $\boxed{\frac{44}{15}}$.