Since the cross section of a disk is the area of a circle, the volume of each disk is the area multiplied by its thickness. If the axis of revolution is the boundary of the plane region and the cross sections are taken perpendicular to the axis of revoltion, then the disk method is the way to go if you want to find the volume of the solid. Now let's learn about finding the volume of solids by using the disk method.
#DISK GRAPH CALCULS HOW TO#
We'll be using a calculator for this example just so that you know how to do it on it.įnInt((cosx-sinx),x,0,pi/4) + fnInt((sinx-cosx),x,pi/4,pi/2) = 0.828įind the area of the region bounded by andįind the area of the region bounded above by and below by from to Now all we have to do is set up the integrals and solve. One integral that goes from 0 to π/4 and another that goes from π/4 to π/2 There is no up,down,left, or right at the point of intersection so in order to find the area, we will have to split this up into 2 different integrals. In this case, from -2 to 4 since they are the y values in which both of the curves intersect.įind the area bounded by the graphs of theses functions in the graph provided below. The limits will also be y values so the limits will be going from down to upwards. The curves are in terms of y so we will be formula for the area in terms of y which is the right function minus the left function. Plug into the formula and we get ->įind the area bounded by the graphs of theses functions provided in the graph below. The points of intersection would be at x = 0 and at x = 1.
Now that we have the basics down, let's try a few examples.įind the area bounded by the graphs of the functions y = x^1/2 and y = x^2
Since the limits are the points where both curves intersect, all we have to do is set both of the curves equal to each other and solve for x or y depending on the case. If we are given the functions but not the limits, do not worry. The second case in which we find the area between curves is the right function minus the left function as presented in this picture -> The first case in which we find the area between curves is the upper function minus the lower function as presented in this picture -> The formula for this is represented as