Calculus 6.3

1.

The graph of y = f{z) between the lines I = {land I = b is TOP: 3:113} rotated around the line 1: = Q to form a solid, as shown in the Line: I": K figure [where K = Q]. 1|.I'I.I'hioh of the following integrals represents the volume of this solid? b of 1r[f[z] After: each slice Is a drole b of 2m[f{m} Q]dz b O] Eiffel)\": O [shzni 31] a: A solid is contructed so that one side is the region between the y=f(x) lines @ = a, x = b, the graph of y = f(@ ) and the x-axis, and the cross-sections of the solid perpendicular to the x-axis are rectangles with base 7 (as shown in the figure). Which of the following integrals represents the volume of this solid? O 7(f(x) )' dx each slice is a rectangle b O 7f(x) dx o *(f(z))? dx O 7r(f(x) )' dxThe graph of y = f(@) between the lines c = a and > = bis Top: y=f(x) rotated around the line y = 9 to form a solid, as shown in the figure (where K = 9). y Line: y= K Which of the following integrals represents the volume of this solid? K b X O 2xx f(x) - 9 dx b b each slice is a circle 7\\(f(x))2 - 81 dx b o / n(f(x) )2 dx b *(f(x) - 9)2 dxA solid is constructed between the graphs of y = f() and Top: y=f(x) y = g(x) and the lines _ = a and a = b so that the cross- sections perpendicular to the x-axis are circles, as shown in the Bottom: y=g(x) figure. Which of the following integrals represents the volume of this solid? X "[(f(x)2 - ((z)2 dx a b each slice is a circle b 4 (f(x) - g(x) )2 dx a h n (f(x))2 - (g(x))2 dx b n(f(x) - g(x) )' dxThe region between the lines _ = a and c = b, and the graphs of Top: y=f(x) y = f(x) and y = g(I) is rotated around the x-axis to form a Bottom: y=g(x) solid, as shown in the figure. Which of the following integrals represents the volume of this solid? b O 2xx[f(x) - g(x)] dx b on(f(z) - g(x)) di b T(fz))? - (9(z))? da (f(x))2 - (9(x)) dx a