Integral Test, Convergence, Infinite Series - Calculus
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YouTubeDrOfEng
Integral Test, Convergence, Infinite Series - Calculus
The integral test determines if an infinite series converges or diverges by comparing it to an improper integral. The test applies if the series' corresponding function, (f(x)), is positive, continuous, and decreasing on the interval ([1,infty )). If the improper integral (int _{1}^{infty }f(x),dx) converges to a finite value, then the series ...
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Integral Test Examples
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MathxMatrix on Instagram: "The Lebesgue integral: a smarter way to calculate the area under a curve. While the traditional Riemann integral (what we learn in school) breaks area into vertical strips, the Lebesgue integral breaks it into horizontal slabs. For "nice" functions, they give the same answer. But Lebesgue is more powerful-using Measure Theory to handle "pathological" or jagged functions where traditional calculus fails. Original creation by @abidebyreason (also on YT)"
1:28
MathxMatrix on Instagram: "The Lebesgue integral: a smarter way to calculate the area under a curve. While the traditional Riemann integral (what we learn in school) breaks area into vertical strips, the Lebesgue integral breaks it into horizontal slabs. For "nice" functions, they give the same answer. But Lebesgue is more powerful-using Measure Theory to handle "pathological" or jagged functions where traditional calculus fails. Original creation by @abidebyreason (also on YT)"
Instagrammathxmatrix
5.1K views6 days ago
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