Volumes Of RevolutionWatch
if u have Y, and its rotating around the X-axis, then its: Pi * integral Ysquared.dx
if its round the y axis, u work out x and its Pi*integral Xsquared.dy
imagine the area under a curve being split up into lots of little strips. they have length y and witdh dx. as this is rotated the strips for a circular disc of radius y and thicknes dx. the area of a circle is Pi r^2, and the volume wud then be Pi r^2 * width, so in the case of our y's and dx's, the volume of a single strip would be Pi y^2dx.
As we want the whole volume, we need to do it for all the strips between the given areas, so we integrate between the two points, say A and B, as integration put simply is everything added up between given points. Therefore we get INTEGRAL Pi y^2 dx The Pi is just a multiplier, so can be taken out of the integral, so we are left with Pi INTEGRAL y^2 dx. As its between certain points, A is put in the x space, and then we minus the B in the x space to find the volume
Sorry if sum of the maths is a bit weird, the site didnt like the integrals, squares and delta signs
V = (integral max + min) Pi*Y^2dx
and all u do then is look at the equation of the curve your rotating, rearrange it so that it is y^2 = [whatever]
then integrate that new [whatever] for the max and min points, minus the min from the max, and then you have your volume
you usually leave it in Pi to so V = Pi X
Is that right, clearly I dont understand the fundamentals I dont try to, gives me a headache I just remember how to do them.