| 1. | Differentiation under the integral sign is not allowed for improper integrals.
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| 2. | You can differentiate both sides just by adding an integral sign alone.
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| 3. | The main difference is that the integral sign is smaller.
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| 4. | We claim that the passage of the limit under the integral sign is valid.
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| 5. | I'm interested in the formal justification for differentiating under an integral sign.
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| 6. | Then I come along and try differentiating under the integral sign, and often it worked.
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| 7. | See Differentiation under the integral sign.
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| 8. | But the introduction of the integral sign by Leibniz clearly paved the way for a summation sign.
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| 9. | Evaluating a mixture of integrals and derivatives can be done by using theorem differentiation under the integral sign.
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| 10. | It shows the spectacular barred spiral galaxy NGC 6872 that is shaped like an " integral sign ".
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