-x² xe* dx -00

Q: Evaluate the definite integral by the limit definition. (x² + 2) dx

A:

Q: + 2c det dx

A: The integral is convergent. We will solve it using basic integral Formulae.

Q: Determine whether each integral is convergent or divergent. Evaluate those that are convergent. x²…

A: according to the problem, we have

Q: Express the limit as a definite integral on the given interval. im. (4(x;") - 3x;JAx, [2, 7] i = 1 7…

A: By limit definition of a definite integral, limn→∞∑i=1nfxi*∆x=∫ab f(x)dx  where ∆x=b-an and…

Q: Determine whether the integral is divergent or convergent. If it is convergent, evaluate it. If not,…

A: Given integral I=∫3∞xe-x2dx

Q: Determine whether the integral is divergent or convergent. If it is convergent, evaluate it. If not,…

A: Given,

Q: Determine whether the integral is divergent or convergent. If it is convergent, evaluate it. If it…

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Q: Use correct notation to evaluate the improper integral and determine if it converges and diverges.…

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Q: Determine whether the integral is divergent or convergent. If it is convergent, evaluate it. If not,…

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Q: Use the Comparison Theorem to determine whether the integral is convergent or divergent. arctan(x)…

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Q: Determine whether the integral is divergent or convergent. If it is convergent, evaluate it. If not,…

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Q: Determine whether the integral is divergent or convergent. If it is convergent, evaluate it. If not…

A: In this question we have to find whether the Integral is divergent or convergent.

Q: Determine whether the integral is divergent or convergent. If it is convergent, evaluate it. If not,…

A: Here this question based on improper integral

Q: Determine, with justification, whether the integral below converges or diverges. dx x15-|sin a|…

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Q: Evaluate the definite integral: 6/x with the upper limit being 5 and lower limit 1

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Q: Use the Comparison Theorem to determine if the following integral converges or diverges. x2 х* — 2

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Q: Determine whether the integral is divergent or convergent. If it is convergent, evaluate it. If it…

A: ∫210   6dx/(x-4)2 [-6(x-4)-1 ]102 [-6/(x-4)]102 -6/(10-4) +6/(2-4) -6/6 +6/(-2) -1-3 ∫210…

Q: Evaluate the definite Integral by the limit definition. (x2 + 4) dx

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Q: ' Determine whether the integral is divergent or convergent. If it is convergent, evaluate it. If…

A: Given integral can be written as

Q: Investigate if the integral, is c is convergent or not. Justify your answer.

A:

Q: Determine whether the integral is convergent or divergent. If it is convergent, evaluate it. (If the…

A: Solution:-Given ∫6∞e-1/xx2dxPut 1x=u⇒-1x2=dudx⇒-1x2dx=dulimt→∞∫6t-e-udu⇒limt→∞ e-u-16t⇒limt→∞e-1/26t…

Q: (a) '8 dx 2

A: (a)∫268 dx=[8x]26We know that ∫k dx=kx+C            = 8*6 - 8*2            = 32

Q: dx 2. (x-1)% (x- 1)

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Q: Determine whether the integral is divergent or convergent. If it is convergent, evaluate it. If not,…

A: The given improper integral is ∫8∞xe-2xdx. The improper integral ∫8∞xe-2xdx can be rewritten as…

Q: Determine whether the integral is convergent or divergent. If it is convergent, evaluate it. (If the…

A: First we will use the comparison test to show that the given in trivial is convergent and then we…

Q: Use the Comparison Theorem to determine whether the integral is convergent or divergent. 00…

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Q: Express the limit as a definite integral on the given interval. lim Ax [О, 6] 9 + X; i = 1 dx

A: The answer is found in step-2

Q: Determine whether the integral is convergent or divergent. If it is convergent, evaluate it. x2 38 9…

A: Consider the given integral, I=∫-∞∞x29+x6dx Calculate the above integral.   Put t for x3 in the…

Q: Determine whether the integral is convergent or divergent. x arctan(x) 00 11 dx (1 + x2)² convergent…

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Q: 1 dx (r-2)2 а.

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Q: Determine whether the integral is divergent or convergent. If it is convergent, evaluate it. If not,…

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Q: Show that the integral is either Convergent or Divergent. If it is convergent evaluate the integral.…

A: To determine the value of the integral.

Q: Determine whether the integral is divergent or convergent. If it is convergent, evaluate it. If not,…

A: The given integral,                ∫-∞182x-32dx

Q: Determine whether the integral is convergent or divergent. x arctan(x) 00 11 dx (1 + x2)2 convergent…

A: Given integral, I=∫0∞11xtan-1x1+x22dx Used formulas, ddxtan-1x=11+x2ddxx=1…

Q: Evaluate the definite integral by the limit definition.

A: Given: ∫031-2x2dx

Q: dx 3-4X

A: We  have to determine the given series is convergent or divergent

Q: Use the Comparison Theorem to determine whetherthe integral is convergent or divergent.

A: To determine whether the integral is convergent or divergent.

Q: Determine whether the integral is divergent or convergent. If it is convergent, evaluate it. If not…

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Q: Ve dx -2 0.

A: If the limit is finite and exist then the integral is convergent .

Q: 4 dx x2 + 16

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Q: Use the definition of the definite integral as a limit of a sum to evaluate (x² – 4x - 2) dx -2

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Q: Express the limit as a definite integral on the given interval. lim 2 x;)?+9 -ах, [1,4] (x;")² + 9'…

A: Use;∫abf(x) dx =limn→∞ ∑n=1n f(xi) ∆x                       over the given interval [a, b].

Q: Evaluate the integral. If the integral is not convergent, answer "divergent." e 1+e2x

A: ∫0∞ex1+e2xdx Consider, ∫ex1+e2xdx=∫ex1+ex2dx Now put, ex=t⇒ex=dtdx⇒ex dx=dt

Q: Write the improper integral which is represented by the following limit. 2x dx lim C-2 Show that the…

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Q: use the Comparison Theorem to determine whether the integral is convergent or divergent. ∫∞0…

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Q: dx .1 ех — 1

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Q: Determine whether the integral is divergent or convergent. If it is convergent, evaluate it. If not,…

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Q: Evaluate the integral if it converges and enter the exact value. If the integral diverges, indicate…

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Q: Use the Comparison Theorem to determine whetherthe integral is convergent or divergent.

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Q: Evaluate the definite integral by the limit definition

A: ∫268dxFormula:∫abcdx=cxab=cb-a   , where c is any constant.

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.