Mathematics, 18.12.2019 05:31 datands
Use the general slicing method to find the volume of the following solids. the solid whose base is the region bounded by the curves y=x² and y=2−x², and whose cross sections through the solid perpendicular to the x-axis are squares
Answers: 1
and the lower bounding curve 
, which has solutions x = ±1. 
![V=\int\limits^{1}_{-1} {(2-2x^2)^2} \, dx\\\\V=\int _{-1}^14-8x^2+4x^4dx\\\\V=\int _{-1}^14dx-\int _{-1}^18x^2dx+\int _{-1}^14x^4dx\\\\V=\left[4x\right]^1_{-1}-8\left[\frac{x^3}{3}\right]^1_{-1}+4\left[\frac{x^5}{5}\right]^1_{-1}\\\\V=8-\frac{16}{3}+\frac{8}{5}\\\\V=\frac{64}{15}](/tpl/images/0423/7328/f0e6b.png)
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Use the general slicing method to find the volume of the following solids. the solid whose base is t...
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