Question: a) When the graph of \(f(x)=x^{2}\) is rotated about the horizontal line \(y=L\) for \(0 \leq x \leq 2\), the volume obtained depends on the value \(L\) :

\[V(L)=\int_{0}^{2} \pi\left(x^{2}-L\right)^{2} d x=\]

b) What value of \(L\) minimizes the volume in part a)? \(L=\)

c) When the graph of any function \(y=f(x)\) is rotated about the horizontal line \(y=L\) for \(a \leq x \leq b\), the volume obtained depends on \(L\) :

\[V(L)=\int_{a}^{b} \pi(f(x)-L)^{2} d z=\]

d) What value of \(L\) minimizes the volume in part \(c\) )? \(L=\)

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