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| Applications of Definite Integrals |
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| Let y = f (x) be a curve. The area bounded by y = f (x), x-axis and the ordinates at x = a and x = b is given by |
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| (ii) The area bounded by the curve x = f (y) |
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| y = axis and the abscissae at y = c and y = d is given by |
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| Note 1: The area bounded by the curves f(x) and g(x) and the ordinates x = a and x = b is given by |
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| Note 2: If curve f (x) lies above the x-axis and g (x) lies below the x-axis then area bounded by f (x) and g (x) is |
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| Note 3: If f (a) and f (b) are opposite in sign then the curve crosses the x-axis say at c. |
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| Then the area bounded the curve f (x), x-axis and the ordinates x = a and x = b is |
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| Example: |
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| Find the area of the region between the X-axis and the graph of
f(x) = x3 - x2 - 2x -1
≤ x < 2. |
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| Solution: |
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| Let us find the values of x in the given interval, for which |
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| f(x) = 0 |
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| x3 - x2 - 2x = 0 |
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| x(x2 - x - 2) = 0 |
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| Partition the domain [-1, 2] to subintervals [-1, 0] and [0, 2] |
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