3.5.10 Manipulating Integrals in Symbolic FormWhen Mathematica cannot give you an explicit result for an integral, it leaves the integral in a symbolic form. It is often useful to manipulate this symbolic form. | Mathematica cannot give an explicit result for this integral, so it leaves the integral in symbolic form. | |
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Integrate[x^2 f[x], x]
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| Differentiating the symbolic form gives the integrand back again. | |
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| Here is a definite integral which cannot be done explicitly. | |
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Integrate[f[x], {x, a[x], b[x]}]
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| This gives the derivative of the definite integral. | |
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| Here is a definite integral with end points that do not explicitly depend on x. | |
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defint = Integrate[f[x], {x, a, b}]
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| The partial derivative of this with respect to u is zero. | |
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| There is a non-trivial total derivative, however. | |
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