Double integrals
DOWNLOAD
FREE
|
Some applications double integrals
Area The area of a region R in the xy-plane is given by [Equation goes here - download the original pdf to see it.] Volume beneath a surface The volume beneath the surface [Equation goes here - download the original pdf to see it.] , where [Equation goes here - download the original pdf to see it.] , above a region R in the xy-plane is [Equation goes here - download the original pdf to see it.] Total mass of a region Let [Equation goes here - download the original pdf to see it.] be the density of a sheet lying in the xy-plane, then the total mass, M, of the region R of this sheet is Equation goes here - download the original pdf to see it.] Centre of mass Where[Equation goes here - download the original pdf to see it.] be the density of a sheet lying in the xy-plane as above, the centre of mass, [Equation goes here - download the original pdf to see it.] , of the region R of this sheet is given by [Equation goes here - download the original pdf to see it.] Moments of inertia As above, where [Equation goes here - download the original pdf to see it.] be the density of a sheet lying in the xy-plane, the moments of inertia, [Equation goes here - download the original pdf to see it.] , about the x- and y-axes respectively are [Equation goes here - download the original pdf to see it.]
|
Contents of
Double integrals
1 Double integral
2 Evaluation of a double integral
3 Some applications double integrals
4 Change of variables
5 The double integral in polar coordinates
|
