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.

Examples:

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