Here we use the formula
substitute into V formula. Set the limits to a and -a (x intersections which enclose the upper area).
Find the volume of the solid generated by revolving about the x-axis the region bounded by the x-axis and the upper half of the ellipse
x^2/a^2 + y^2/b^2 = 1
(and thus find the volume of a prolate spheroid)
Here a and b are positive constants with a>b
Volume of the solid of revolution?
Okay, so this one is tripping me up a bit... here's what I've done:
I tried to solve for y and got --
y = square root(b^2(1 - x^2/a^2)) or y = b*sqrt(1 - x^2/a^2)
I thought I would need to square the function and ultimately multiply by pi:
pi int_a^b (b^2(1-x^2/a^2) dx and I moved the b^2 to the beginning with pi and integrated to get:
b^2* pi [ x - x^3/3a^2]
so my final answer, keeping the b and a...
b^2*pi[(b-(b^3)/(3a^2))-(a-(a^3)/(3a^2))]
unfortunately this is not the correct answer. any help?? thanks!