( v ) Area bounded by two curves y = F ( x ) and y = G ( x ) between x = a and x = b is given by
( vi ) Area bounded by two curves x = f ( y ) and x = g ( y ) between y = c
and y = d is given by
( vii ) If F ( x ) ≥ . G ( x ) in [ a , c ] and F ( x ) ≤ G ( x ) in [ c , d ], where a < c < b , then area of the region bounded by the curves is given as
Area of Curves Given by Polar Equations
Let f ( θ ) be a continuous function , θ ∈ ( a , α ), then the are t bounded by the curve r = f ( θ ) and radius α , β ( α < β ) is