Area bounded by the curve

Jun 15, 2020, 16:45 IST

Area bounded by the curve

Definition :-The area is the quantity which is used to express the region occupied by the two-dimensional shapes in the planar lamina.

Formula description :
Case I : When two curves intersect at two points and their common area lies between these points.

are two curves which intersect at P(x = a) and Q (x = b), and their common area lies between P and Q. then their

Case : II When two curves intersect at a point and the area between them is bounded by x-axis.

are two curves which intersect at P(x = c) and meet x-axis at A(x = a) and B(x = b) respectively, then area between them and x-axis is given by

Example 1 :-Using the method of integration find the area bounded by the xurve |x| + |y| = 1

Solution :-
So, we can write |x| + |y| = 1

Since the curve symmetrical about x & y – axis
Required Area = 4 × Area AOB

Area AOB

Where
X + y = 1
Y = 1 – x
Therefore,

Hence ,

Example 2 :-The area between the curves

Solution :-