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Unformatted text preview: 2. The definite integral from a to b of f(x) is the net change in F , meaning it is F(b) – F(a) , where F’ = f . So, the net change in F , the antiderivative of f , is equal to the integral of f(x) from a to b . Example 1 h(x) = ∫3 2 1 4 sinh x tdt , find h’(x) . dx d h(x) = ∫3 2 1 4 sinh x tdt dx d h’(x) = ∫3 2 1 4 sinh x tdt dx d h’(x) = 3x 2 sinh1 4(x 3 ) Example 2 ∫ 5 2 5 dx x ∫ 5 2 5 dx x = 5 2 5 ln 1  5 x ∫ 5 2 5 dx x = 5 ln 1 (5 5 – 5 2 ) = 5 ln 1 (3125 – 25) = 5 ln 1 (3100)...
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This note was uploaded on 02/04/2011 for the course MATHEMATIC 33 taught by Professor Qian during the Winter '99 term at Hong Kong Shue Yan.
 Winter '99
 qian
 Derivative

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