6.2. USING DEFINITE INTEGRALS TO FIND VOLUME
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(b) Set up a definite integral whose value is the exact area of R.
(c) Set up a definite integral whose value is the exact volume of the solid of
revolution generated by revolving R about the x-axis.
(d) Set up a definite integral whose value is the exact volume of the solid of
revolution generated by revolving R about the y-axis.
(e) Set up a definite integral whose value is the exact volume of the solid of
revolution generated by revolving R about the line y = 2.
(f) Set up a definite integral whose value is the exact volume of the solid of
revolution generated by revolving R about the x = −1.
3. Consider the finite region R that is bounded by the curves y = 1 +
1
2 (x − 2) 2 , y =
1
2 x 2 ,
and x = 0.
(a) Determine a definite integral whose value is the area of the region enclosed by
the two curves.
(b) Find an expression involving one or more definite integrals whose value is the
volume of the solid of revolution generated by revolving the region R about the
line y = −1.
(c) Determine an expression involving one or more definite integrals whose value
is the volume of the solid of revolution generated by revolving the region R
about the y-axis.
(d) Find an expression involving one or more definite integrals whose value is the
perimeter of the region R.