The volume of the solid obtained by rotating the region bounded by the curves y=sqrt(25 - x^2), y=0, x=2,x=4 , about x axis, can be evaluated using the washer method.
V = int_a^b pi*(f^2(x) - g^2(x)) dx, f(x)>g(x)
Since the problem provides you the endpoints x=2,x=4 , you may find the volume such that:
V = int_2^4 pi*(sqrt(25 - x^2) - 0)^2 dx
V = pi*int_2^4 (25 - x^2)dx
V = pi*(int_2^4 25 dx - int_2^4 x^2 dx)
V = pi*(25x - x^3/3)|_2^4
V = pi*(25*4 - 4^3/3 - 25*2 + 2^3/3)
V = pi*(50 - 56/3)
V = pi*(150-56)/3
V = (94*pi)/3
Hence, evaluating the volume of the solid obtained by rotating the region bounded by the curves y=sqrt(25 - x^2), y=0, x=2,x=4, about x axis , using the washer method, yields V = (94*pi)/3 .
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