Determine whether the improper integral diverges or converges. O converges O diverges Evaluate the integral if it converges. (If the quantity diverges, enter DIVERGES.) Need Help? Read It Watch it Master It

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Q: How do I do this one?

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A: The given integral is ∫01211xpdx

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Q: Comparison Test Determine whether the following integrals converge or diverge.

A: Determine whether the following integrals converge or diverge.

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A: Use integral test for checking the convergence of series

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A: Given : ∫2∞1x3dx

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Q: Improper Integrals Determine if the following integral converges or diverges. If the integral…

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A: Evaluate the integral .

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Q: Determine if the improper integral is convergent or divergent, and calculate its value if it is…

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A: Given integral, ∫-88dxx3

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Q: 1- x evaluate the improper integral dx. Does it converge V1 – x2 diverge? Justify your claim.

A: ∫-111-x1-x2dx=∫-1111-x2-x1-x2dx=∫-1111-x2dx-∫-11x1-x2dx=arcsinx-11-0=π

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Q: 5. Comparison Test Determine whether the following integrals converge or diverge. dx

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A: Given, I=∫0∞5e-5xdx

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Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.