Recent content by ehrenfestcq
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Graduate How to Derive an Integral Formula with an Infinite Upper Limit?
Thanks! Yes, I considered Leibniz's rule. What had thrown me off was the fact that the upper limit of integration is ∞. This appears to work just fine, although I am concerned with the notion that \frac{d∞}{dx} should be zero. Might I instead handle this by integrating on [x,α] and then...- ehrenfestcq
- Post #3
- Forum: Calculus
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Graduate How to Derive an Integral Formula with an Infinite Upper Limit?
Please derive the right-hand side from the left. If anyone could shed some light on this I would be grateful. \frac{d^{2}}{dx^{2}}\int_x^{∞}f(x,z)g(z)dz = \int_x^{∞}f_{xx}(x,z)g(z)dz - g(x)(f_{z}(x,x) + 2f_{x}(x,x)) - f(x,x)g'(x) Please, if you can, provide a detailed explanation of...- ehrenfestcq
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- Formula Integral Interesting
- Replies: 2
- Forum: Calculus