Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis.
y = 6x^2, x = 1, y = 0, about the x-axis
V = integral (low: a, up: b) A(x) dx
2007-07-26 14:58:48 · 2 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
V = π∫(0 to 1) y^2 dx
= π∫(0 to 1) 36x^4 dx
= π [36 x^5 / 5] [0 to 1]
= π (36 / 5 - 0)
= 36π / 5.
2007-07-26 15:03:29 · answer #1 · answered by Scarlet Manuka 7 · 0⤊ 0⤋
The volume will be:
V=2Ï(â«6x²dx)²
To find the limits of integration, first determine what x is when
y = 0 by setting the function 6x² = 0 and solving for x. Once that is done, just take the smaller of the two x's and that will be your lower limit and the larger of the two will be your upper limit.
2007-07-26 22:07:30 · answer #2 · answered by Aaron 2 · 0⤊ 0⤋