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Mathematics
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Session Definite Integrals –1
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Session Objectives Fundamental Theorem of Integral Calculus Evaluation of Definite Integrals by Substitution Class Exercise
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Fundamental Theorem of Integral Calculus Let F(x) be any primitive (or antiderivative) of a continuous function f(x) defined on an interval [a, b]. Then the definite integral of f(x) over the interval [a, b] is given by ‘a’ is called the lower limit and ‘b’ the upper limit. Note: The value of a definite integral is unique.
![Fundamental Theorem of Integral Calculus Let F(x) be any primitive (or antiderivative) of a continuous function f(x) defined on an interval [a, b].](http://images.slideplayer.com./26/8387253/slides/slide_4.jpg "Then the definite integral of f(x) over the interval [a, b] is given by ‘a’ is called the lower limit and ‘b’ the upper limit. Note: The value of a definite integral is unique..")
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Example - 1
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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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Example - 5
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Solution Cont.
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Example - 6
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Evaluation of Definite Integrals by Substitution Now find the result using the fundamental theorem.
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Example - 7
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Example - 8
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Solution Cont.
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Example - 9
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Solution Cont.
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Example - 10
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Solution Cont.
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Example - 11
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Solution Cont.
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Thank you
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