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Mathematics
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Session Definite Integrals - 3
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Session Objectives Definite Integral as the Limit of a Sum
Areas of Bounded Regions Class Exercise
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Definite Integral as the Limit of a Sum
OR
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Example - 1
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Solution Cont.
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Example - 2
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Solution Cont.
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Example - 3
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Solution Cont.
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Example - 4
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Solution Cont.
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Example - 5
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Solution Cont.
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Areas of Bounded Regions
1. Let f(x) be a continuous function defined on the interval [a, b]. Then, the area bounded by the curve y = f(x), x-axis and the ordinates x = a, x = b is The area bounded by the curve x = f(y), y-axis and the abscissae y = c, y = d is
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Areas of Bounded Regions Cont.
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Example - 6
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Solution Cont.
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Example - 7
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Solution Cont.
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Solution Cont.
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Example - 8 Solution: The given curves are
(i) and (ii) intersect at (1, 0) and (0, 1).
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Solution Cont.
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Example - 9
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Solution Cont.
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Example - 10 Solution: The given curves are
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Solution Cont.
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Solution Cont.
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Solution Cont.
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Example - 11
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Solution Cont. x' x y y' O (1, 0) x2 + y2 = 1 (x - 1)2 + y2 = 1
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Solution Cont.
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Solution Cont.
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Thank you
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