Problem
4. $[-1 / 2$ Points $]$ DETAILS SCALC9 5.1.010. MY NOTES ASK YOUR Set up an integral representing the area $A$ of the region enclosed by the given curves. \[ \begin{array}{l} x=y^{4}, x=2-y^{2} \\ A=\int_{-1}(\square) d y \\ \text { Need Help? Read It } \end{array} \] Read It Submit Answer
Solution
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: \(\boxed{\frac{44}{15}}\).
