Integrals - are given the initial condition and asked to...

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6.1: Antiderivatives Greg Kelly, Hanford High School, Richland, Washington
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First, a little review: Consider: 2 3 y x = + then: 2 y x = 2 y x = 2 5 y x = - or It doesn’t matter whether the constant was 3 or -5, since when we take the derivative the constant disappears. However, when we try to reverse the operation: Given: 2 y x = find y 2 y x C = + We don’t know what the constant is, so we put “C” in the answer to remind us that there might have been a constant.
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If we have some more information we can find C. Given: and when , find the equation for . 2 y x = y 4 y = 1 x = 2 y x C = + 2 4 1 C = + 3 C = 2 3 y x = + This is called an initial value problem . We need the initial values to find the constant. An equation containing a derivative is called a differential equation . It becomes an initial value problem when you
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Unformatted text preview: are given the initial condition and asked to find the original equation. Integrals such as are called definite integrals because we can find a definite value for the answer. 4 2 1 x dx 4 2 1 x dx 4 3 1 1 3 x C + 3 3 1 1 4 1 3 3 C C - + + 64 1 3 3 C C-+-63 3 = 21 = The constant always cancels when finding a definite integral, so we leave it out! Integrals such as are called indefinite integrals because we can not find a definite value for the answer. 2 x dx 2 x dx 3 1 3 x C + When finding indefinite integrals, we always include the plus C....
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This note was uploaded on 04/12/2011 for the course PHYS 1320 taught by Professor Staff during the Spring '11 term at North Texas.

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Integrals - are given the initial condition and asked to...

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