(i) The area of the region bounded by the curve

`y = f(x)`, X-axis and the lines `x =a, x = b` is given by

Area `= int_a^b y dx = int_a^b f(x) dx`







(ii) The area of the region bounded by the curve

`x = phi (y)`, Y-axis and the lines `y = c, y =d` is given by

Area `= int_c^d x dy = int_c^d phi (y) dy`







(iii) The area of the region enclosed between the two curves
`y = g (x ), y = f(x)` and the lines `x = a, x = b` is given by

Area `= int_a^b f(x) dx- int_x^b g(x) dx`

`= int_a^b [ f(x) - g(x)] dx`

where, `f(x) ge g(x)` in `[a,b]`







(iv) The area of the region enclosed between the two curves
`x = g(y ), x = f(y)` and the lines

`y = c, y = d` is given by

Area `= int_c^d f(y)dy`

`int_c^d [f(y)- g(y)]dy`,

where, `f (y) ge g (y)` in `[c, d]`

Note : If some part of curves lies below the X-axis, then its area lies in negative side but area cannot be negative. Therefore, we
take its modulus.