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