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प्रश्न
Find, by integration, the volume of the solid generated by revolving about the y axis, the region enclosed by x2 = 1 + y and y = 3
उत्तर
V = `int_"a"^"b" pix^2 "d"y`
= `int_(-1)^3 pi(1 + y) "d"y`
= `pi[y + y^2/2]_(-1)^3`
=`pi[(3 + 9/2) - (-1 + 1/2)]`
V = `pi[15/2 + 1/2]`
= `pi[16/2]`
= 8π cubic units.
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