**1. Area bounded by a curve**

(i) The area bounded by a Cartesian curve y = f(x), x-axis and abscissa x = a and x = b is given by,

(iii) If the equation of a curve is in parametric form, say x = f(t), y = g(t), then the area =

where t_{1} and t_{2} are the values of t respectively corresponding to the values of a & b of x.

(iv) If the curve be symmetrical and suppose it has n symmetrical portions then total area = n × area of one symmetrical portion

(v) If some part of the curve lies below x-axis then its area is negative then area must be calculated separately using modules sign. For example

**2. Symmetrical area**

If the curve is symmetrical about a coordinate axis (or a line or origin), then we find the area of one symmetrical portion and multiply it by the number of symmetrical portions to get the required area.

**3. Area between two curves**

(i) When two curves intersect at two points and their common area lies between these points. If y = f_{1}(x) and y = f_{2}(x) are two curves where f_{1}(x) > f_{2}(x) which intersect at two points A (x = a) and B (x = b) and their common area lies between A & B, then their

(ii) When two curves intersect at a point and the area between them is bounded by x-axis. If y = f_{1}(x) and y = f_{2}(x) are two curves which intersect at P(α, β) & meet x-axis at A(a, 0), B(b, 0) respectively, then area between them and x- axis is given by

✅ 12th grade math formulas ⭐️⭐️⭐️⭐️⭐

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