Question

(1 point) Find the volume of the solid obtained by rotating the region bounded by the given curves below about the line x=5.

y=x^2,y=5x

Volume =

Answer 1

we have y = x² and y = 5x hence we can write,

Hence we can say that x ranges from x = 0 to x = 5

It means we have to find the volume of the solid obtained by rotating the region bounded by the curve y = x² and y = 5x between x = 0 and x = 5 about x = 5

we know that according to shell method volume of the solid obtained by rotating the region bounded by the curve y = f(x) and y = g(x) between x = a and x = b about x = k is given by,

   -------------------------------------------------------1)

where,

f(x) > g(x) means f(x) is the top curve above g(x) between x = a and x = b

we have to rotate the region bounded by given curves between x = 0 and x = 5 hence we have a = 0 and b = 5

we can see that y = 5x is the top curve above y = x² between x = 0 and x = 5 hence we have f(x) = 5x, g(x) = x²

Also we have to rotate about x = 5 means we have k = 5

Hence according to shell method formula given in equation 1) we can write volume is given by,