If you are just finding the area between f(x) and the x-axis, it is this simple. What is more complicated is when you need to find the volume of a rotating solid between two or three functions. In that case, you would need to use one of several methods. The three most common ones I have heard of can all work, but which is easiest depends on the problem. The methods are called the "disc" method, in which you essentially "slice" the solid to be calculated into discs, and then add them all up, the "shell" method, in which you "unwrap" the solid (like an onion, as my calculus teacher used to say) and add up the layers, or the "hole" method, in which you take the integral of the entire thing to find the volume, then find the volume of the hole, and subtract that from the whole. All of them require taking the integral in order to find the volume. I don't blame you if you find this confusing right now. You will probably learn it soon, though.Hi thanks so much for your help. This is the answer that I got originally however did not think that it could be that simple and that I was meant to go further with it to actually get the area?
It's almost as easy if you understand how to use double/triple integrals! But of course, you need a function with more than one variable!If you are just finding the area between f(x) and the x-axis, it is this simple. What is more complicated is when you need to find the volume of a rotating solid between two or three functions. In that case, you would need to use one of several methods. The three most common ones I have heard of can all work, but which is easiest depends on the problem. The methods are called the "disc" method, in which you essentially "slice" the solid to be calculated into discs, and then add them all up, the "shell" method, in which you "unwrap" the solid (like an onion, as my calculus teacher used to say) and add up the layers, or the "hole" method, in which you take the integral of the entire thing to find the volume, then find the volume of the hole, and subtract that from the whole. All of them require taking the integral in order to find the volume.
by Robert Keim
by Jake Hertz
by Jake Hertz