The integral I = 40 dx 1 + is [Hint: You may need to use the Mean Value Theorem for Derivatives] O convergent and its value is 0 divergent O convergent and 10 r s I S 40 convergent and 40 < I convergent and I< 10

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A: Solution is given as below:

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A: We have to find if the given integral is convergent or divergent.For this we will evaluate the…

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A: Please see the below picture for detailed solution.

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Q: Evaluate the integral. If the integral is convergent, enter its exact value. If it divergent, enter…

A: .........(1)Substitute      ..........Put it back in equation 1

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A: As per our guidelines, we are supposed to answer only one question. Kindly repost other questions as…

Q: Use a comparison test to determine whether I (ln(x) — 1) dx converges or diverges.

A: (i) If f(x)≤g(x),∀x∈[a,∞) and ∫a∞g(x)dx is convergent,  then ∫a∞f(x)dx is convergent. (ii) If…

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Q: (2) Determine whether each improper integral converges or diverges. If it is convergent find the…

A: According to bartleby guidelines we are supposed to do the first one of multiple questions kindly…

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Q: Use a summation to find the integral from 0 to 4 of f(x) 2x + 1.  Then check it using the power rule…

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Q: dx is convergent V2 1 True False 1, 8.

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Q: 2. For p>1, is S dx convergent? Inx xP

A: To show that whether the given integral is convergent for p&gt;1.

Q: Find J Ta-xdx

A: Given integral is ∫x1−x23dx. We have to solve the given integral. Substitute 1−x2=u…

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.