Summary of Class 12 Maths Application of Integrals
Application of Integrals
1. Let f(x) be a continuous function defined on [a,
b]. Then, the area bounded by the curve y = f(x), the x-axis
and the lines x = a and x = b (b > a),
is given by 
or 
.
2. If the area under the curve y = f(x) is
below the x-axis, we take the absolute value of 
|
as area is a positive quantity.
3. The area of the region bounded by the curve x = g(y),
the y-axis and the lines y = c and y = d, is
given by 
dy or 
dy.
4. Sometimes, it may happen that some portion of the curve is above x-axis and some is below the x-axis as shown in
the figure. Let A1 be the area below the x-axis and A2
be the area above the x-axis. Therefore, the area A bounded by the curve
y = f (x), x-axis and the ordinates x = a
and x = b is given by A = |A1| + A2.
