Evaluate the following improper integrals:(a) βˆ«βˆ’βˆž0​exdx(b) ∫1βˆžβ€‹... | Filo
Evaluate the following improper integrals:(a) βˆ«βˆ’βˆž0​exdx(b) ∫1βˆžβ€‹... | Filo
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SOLVED:The integrals converge. Evaluate the integrals without using tables. ∫0^1 x lnx d x
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Evaluate the improper integral \int _ { 0 } ^ { \infty } x e ... | Filo
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πŸ”₯ Day 117 β€” Can you solve this? Evaluate the integral (a > 0, b β‰₯ 0): βˆ«β‚€^∞ e^(βˆ’a x) Β· sin(bx) / x dx It looks tough β€” but a parameter derivative makes it collapse πŸ“‰ Differentiate with respect to b, use the Laplace transform of cos(bx), then integrate back. πŸ‘‰ Hint: Fβ€²(b) = βˆ«β‚€^∞ e^(βˆ’a x) cos(bx) dx = a/(aΒ² bΒ²). Integrate in b and use F(0) = 0 to nail the constant πŸ‘€ Would you land the exact expression before time runs out? ⏱️ πŸ’­ Drop your answer below πŸ‘‡ βœ… Full step-by-step solution is already
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