Find the volume of the solid obtained by rotating the region enclosed by the curves y = x and y = x^5 about the x-axis, where .

Question

Find the volume of the solid obtained by rotating the region enclosed by the curves y = x and y = x^5 about the x-axis, where  .

anonymous · Answer

This problem requires using the disk method. $$V= pi \int\limits_{a}^{b} f^2(x) - g^2(x) dx$$

In this problem the area bound by the two curves is bound from 0<=x<=1 and since the line y=x is on top it is considered the f(x) and y=x^5 would be g(x). If you insert these values into the equation you get

$$V= \pi \int\limits_{0}^{1} x^2- x^{10}dx$$

from there you would solve the integral to get the equation 
V= pi * [(1/3) x^3 - (1/11) x^11] evaluated from zero to one and it would result in 8pi/33

anonymous · Answer

ohhh. That makes sense.. Just one question; When I asked the question, I forgot to put "where.." x>orequalto 0

anonymous · Answer

would that make any difference in the problem's solution?

anonymous · Answer

nope! becaues the region enclosed by the two lines is already above the x-axis :)

anonymous · Answer

kthanks  (: you're the best!