5. \( y_{1}=x^{2}-6 x \)
\[
y_{2}=0
\]
6.
\[
\begin{array}{l}
y_{1}=x^{2}+2 x+1 \\
y_{2}=2 x+5
\end{array}
\]
7. \( y_{1}=x^{2}-4 x+3 \)
\[
y_{2}=-x^{2}+2 x+3
\]
9. \( y_{1}=3\left(x^{3}-x\right) \)
\[
y_{2}=0
\]
19. \( f(x)=\frac{1}{9 x^{2}}, \quad y=1, \quad x=1, \quad x=2 \)
20. \( f(x)=-\frac{4}{x^{3}}, \quad y=0, \quad x=-3, \quad x=-1 \)
21. \( f(x)=x^{5}+2, \quad g(x)=x+2 \)
22. \( f(x)=\sqrt[3]{x-1}, \quad g(x)=x-1 \)
23. \( f(y)=y^{2}, \quad g(y)=y+2 \)
24. \( f(y)=y(2-y), \quad g(y)=-y \)
25. \( f(y)=y^{2}+1, \quad g(y)=0, \quad y=-1, \quad y=2 \)
26. \( f(y)=\frac{y}{\sqrt{16-y^{2}}}, \quad g(y)=0, \quad y=3 \)
27. \( f(x)=\frac{10}{x}, \quad x=0, \quad y=2, \quad y=10 \)
28. \( g(x)=\frac{4}{2-x}, \quad y=4, \quad x=0 \)
Comparing Methods In Exercises 29 and 30, find the area of the region by integrating (a) with respect to \( x \) and (b) with respect to \( y \). (c) Compare your results. Which method is simpler? In general, will this method always be simpler than the other one? Why or why not?
29. \( x=4-y^{2} \)
30. \( \begin{aligned} y & =x^{2} \\ y & =6-x\end{aligned} \) \( x=y-2 \)
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