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| Summary |
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| If f(x) is a continuous function on the closed interval [a, b], and if |
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| Area function is defined by |
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 If f (x) is a function continuous on [a, b] then |
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| Evaluation of definite integral by changing limits after suitable substitution. |
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| Step I : Let z = g(x) be the desired substitution, dz = g' (x) dx |
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| Step II : when x = a, z = g(a) |
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| x = b, z = g(b) |
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| Properties of definite integrals |
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The area bounded by the curve y = f(x), x-axis, and the ordinates at |
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The area bounded by the curve x = f(y), y - axis and the abscissas |
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| If f(x) is continuous in [a,b] and crosses the x-axis at x = c in (a, b) then the area bounded by the curve, x - axis and x = a and x = b is |
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| Area between y = f(x) and y = g(x), |
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