Applications to Area and Volume
Applications to Area and Volume:
1. Area of the region R in the Cartesian form.
2. Area of the region R in the Polar form.
3. Volume of a solid.
4. Volume of a solid (in polars) obtained by the revolution of a curve enclosing an area A about the initial line is given by
5. If z = f (x,y) be the equation of a surface S then the surface area is given by
Where A is the region representing the projection of S on the xy-plane.
Type-1: Evaluate over a given region
1. Evalaute Where R is the triangle region bounded by the axes of the coordinates and the line
Solution: R is the region bounded by x = 0, y = 0 be the co-ordinate axes and being the straight line through (0,a) and