Working rule for finding out the area:
(i) If curve lies above the x axis completely, then the area is positive but when it lies below x axis completely, then the area is negative, however we have the convention to consider magnitude only.
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(ii) If curve lies on both sides of x axis that is above the x axis as well as below the x axis, then calculate both areas individually and add their modulus to obtain the total area.
Generally if curve y = f(x) crosses the x axis n times when x varies from a to b, then area between y = f(x), x axis and lines x = a and x = b can be given by
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(iii) If curve is symmetrical about x axis, or y axis, or both these, then calculate the area of 1 symmetrical part and multiply it by number of symmetrical parts to obtain the whole area.
Illustration: Find out the area between curves y = x2 + x -2 and y = 2x, for which |x2 + x -2| + | 2x | = |x2 + 3x -2| is satisfied.
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Solution: y = x2 + x - 2 => y = 2x
|x2 + x - 2| + |2x| = |x2 + 3x - 2|
(x2 + x - 2) and 2x have same sign
Therefore the required area
ar (PQR) + ar (ECD)
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