Question

Let ( f(x)=3 cos left(frac{pi}{6} x ight) ) and ( g(x)=3+5 x-x^{2} ). Let ( R ) be the region bounded by the graphs of ( f ) and ( g ), as shown above. a) Find the area of ( R ). b) Region ( R ) is the base of a solid. For this solid, each cross section perpendicular to the ( x )-axis is a square. Write, but do not evaluate, an integral expression that gives the volume of the solid. c) Write, but do not evaluate, an integral expression that gives the volume of the solid generated when ( R ) is revolved about the horizontal line ( y=-3 ).

          Let ( f(x)=3 cos left(frac{pi}{6} x
ight) ) and ( g(x)=3+5 x-x^{2} ). Let ( R ) be the region bounded by the graphs of ( f ) and ( g ), as shown above.
a) Find the area of ( R ).
b) Region ( R ) is the base of a solid. For this solid, each cross section perpendicular to the ( x )-axis is a square. Write, but do not evaluate, an integral expression that gives the volume of the solid.
c) Write, but do not evaluate, an integral expression that gives the volume of the solid generated when ( R ) is revolved about the horizontal line ( y=-3 ).

$Let ( f(x)=3 cos left(fracpi6 x ight) ) and ( g(x)=3+5 x-x^2 ). Let ( R ) be the region bounded by the graphs of ( f ) and ( g ), as shown above. a) Find the area of ( R ). b) Region ( R ) is the base of a solid. For this solid, each cross section perpendicular to the ( x )-axis is a square. Write, but do not evaluate, an integral expression that gives the volume of the solid. c) Write, but do not evaluate, an integral expression that gives the volume of the solid generated when ( R ) is revolved about the horizontal line ( y=-3 ).$

Added by Francis S.

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