Area of Parametric Curves
Let x = φ( t) and y = ψ( t) be two parametric curves, then area bounded by the curve, X-axis and ordinates x = φ( t1), x = ψ( t2) is
Volume and Surface Area
If We revolve any plane curve along any line, then solid so generated is called solid of revolution.
Volume of Solid Revolution 1. The volume of the solid generated by revolution of the area bounded
by the curve y = f( x), the axis of x and the ordinates it being given that f( x) is a continuous a function in the interval( a, b).
2. The volume of the solid generated by revolution of the area bounded by the curve x = g( y), the axis of y and two abscissas y = c and y = d is
d). it being given that g( y) is a continuous function in the interval( c,
Surface of Solid Revolution
( i) The surface of the solid generated by revolution of the area bounded by the curve y = f( x), the axis of x and the ordinates
is a continuous function in the interval( a, b).
( ii) The surface of the solid generated by revolution of the area bounded by the curve x = f( y),
the axis of y and y = c, y = d is in the interval( c, d). continuous function