The limit n lim E /2x + (x; )²Ax i=1 can be expressed as a definite integral on the interval [1, 8] of the form f(x) dx Determine a, b, and f(x). a = ... ... ... b = ... ... f(x) = ... ... ...

Q: Express the limit as a definite integral on the given interval. cos(x¡) Дх, [Зл, бл] Xi lim бл dx…

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Q: n, ]x| fn (x) = - 2m 0, x > 2n | fn (x) cos x dx lim Calculate its limit. What happens if the limit…

A: Write the integral as limn→∞∫-11fnxcosx dx=limn→∞∫-1-12nfnxcosx dx+∫-12n12nfnxcosx dx+∫12n1fnxcosx…

Q: Express the limit as a definite integral on the given interval. [9(x†)3 – 4xj]Ax, [2,9] lim n- 00 i…

A: Express the limit as a definite integral on the given interval.

Q: Express the limit as a definite integral on the given interval. n lim x, In(2 + x,-) Ax, [0, 4] i =…

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Q: Express the limit as a definite integral on the given interval. lim (5(x)3 – 7x]Ax, [2, 6] n- 00 = 1…

A: Consider the given limit and interval. limn→∞ ∑i=1n5xi*3−7xi*Δx and interval=2,6 Now, go through the…

Q: mcory amu LAampIOS 45. Finding an upper limit of an iterated integral Solve for a: 1-x² ¢4-x²-y 4 dz…

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Q: Express the limit as a definite integral on the given interval. lim [9(x;")³ – 4x;]Ax, [2, 8] i = 1…

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Q: 4. Determine if the Mean Value Theorem for Integrals applies to the function f(x) = x³ - 9x on the…

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Q: Express the limit as a definite integral on the given interval. lim X; V 4 + x3 Ax i = 1 [2, 3] n-…

A: Given the limit limn→∞∑i=1nxi4+xi3∆x in the interval [2,3]

Q: Express the limit as a definite integral on the given interval. lim n → ∞  n [2 − 5(xi*)2 + 6(xi*)4]…

A: Given query is to find the integral form of limit.

Q: П 9. In(1+ kx) sin r x(ekz – x – 1) lim \k=2

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Q: Only one of these calculations is correct to evaluate the definite integral Inx dx Select one: Inx…

A: Integral test:  Integrals convergent if the associated limit exists and is a finite number (i.e.…

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

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Q: (4.3) For #17-19, use the limit process to evaluate each definite integral. 4 |(x* +2)dx 17.

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Q: Express the limit as a definite integral on the given interval. [5(x;)3 - 3x;]Ax, [2, 6] n- 00 i = 1…

A: see below the answer

Q: Express the limit as a definite integral on the given interval. lim (2-5(x,)² + 6(x;")³] Ax, [0, 4]…

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Q: 1. Sketch the graph of the function y = f(x) = 3 – V4 – x² over [-2, 2] and use this to evaluate the…

A: Given: The function y=f(x)=3-4-x2,             Interval: [-2,2]             Integral:…

Q: Express the limit as a definite integral on the given interval. n lim -Дх, [1, 3] (x*)2 + 8 i = 1 dx

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Q: Consider , xe¬**dx. What will be the appropriate solution and answer to this improper integral? A.…

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Q: If the integral converges, enter its value. If the integral diverges, enter "diverges" (without the…

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Q: 12.)Express lim E(3(x;,)² – 5x, + 2)Ax as a definite integral on the interval [0,1]. i=1

A: The given expression is: limn→∞ ∑i=1n 3xi2-5xi+2∆x    on interval [0, 1]   The definite integral  on…

Q: Determine if the integral converges or diverges by comparison.

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Q: Express the limit as a definite integral on the given interval. lim n- 00 [4(x;)³ – 4x;"]ax, [(2, 7]…

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Q: At the point of discontinuity on(0, 00), the Fourier Sine integral converges to: OA None f(x+) -…

A: Here  At the point of discontinuity on  0,∞ the Fourier sine integral converges to

Q: 3. Prove that -2/3 dx diverges by showing that х lim -2/3 dx = 00 х

A: Given limit is Since one of the limit of integration is infinite , so we evaluate the limit as…

Q: calculate the limit of ln(x) - (e)^x  x goes to + infinite

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Q: Express the limit as a definite integral on the given interval. lim Σ Σ x;* -ΔΧ, [1,4] 0-700 (x;*)2…

A: To express the given limit as a definite integral.

Q: 4. (a) Explain why the integral (1+ x)3 dx is an improper integral. Determine whether the improper…

A: We have to find out

Q: Evaluate the indefinite integral as an infinite series. | arctan(x2) dx Σ + C n = 0

A: Answer

Q: Express the limit as a definite integral on the given interval. exi Ax 3 + x; lim [0, 4] dx

A: We need convert summation in to integral

Q: Express the limit as a definite integral on the given interval. n -Ax, (x;")2 + 6 [1, 5] lim i = 1 5…

A: Given query is to express the limit as definiye integral.

Q: What is the definite integral represented by the limit lim (+4) Ax, on the interval [-1,1]? n-x •…

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Q: Express the limit as a definite integral on the given interval. cos(x;) lim n-0 i = 1 Дх, [2л, 5л]…

A: Given limn→∞∑i=1ncos(xi)xi∆xi in the interval [2π,5π]We need to express the limit as a  definite…

Q: Find a limit equal to (x2 – 8)dx. 3

A: The integral of some functions are given below. 1)∫x2dx=x33+c2)∫8dx=8x+c Use the above and find the…

Q: Express the limit as a definite integral on the given interval. lim x; In(2 + x²') Ax, [0, 2] i = 1…

A: Given, limn→∞∑i=1nxi ln2+xi2∆x And interval 0, 2

Q: Evaluate the definite integral.

A: ∫012arccosx1-x2 dx Consider, ∫arccosx1-x2 dx Now put, arccosx=t⇒-11-x2=dtdx⇒11-x2 dx=-dt Therefore,…

Q: Express the limit as a definite integral on the given interval. lim [9(x;)³ – 9x;14x, [2, 8] i = 1…

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Q: Express the limit as a definite integral on the given interval. cos X Дх, [Зя, бя] lim 6x X dx 3x

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Q: Express the limit as a definite integral on the given interval. x;* -Ax, (x;')² + 2 lim n- co [1, 6]…

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Q: Express the limit as a definite integral on the given interval. n x* lim (xF)2 + 2 Ax, [1, 7] (x*)2…

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Q: Find the indefinite integral ∫ [arctan(x/2)] / (4 + x2) dx

A: ∫arctanx24+x2dx Now put, arctanx2=t⇒11+x22·12=dtdx⇒11+x24·12=dtdx⇒44+x2·12=dtdx⇒24+x2=dtdx⇒14+x2…

Q: Determine if this improper integral will diverge or converge dx (x² – 1)4/3 1 Apply this in solving:…

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Q: Express the limit as a definite integral on the given interval. lim 8x; + (x;)² Ax, [3, 8] dx

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: 2. Determine if the integral converges or diverges. Part of your grade on this problem depends on…

A: Topic:- integration

Q: Evaluate the indefinite integral as an infinite series. arctan(x5) dx Σ( |)•c n = 0

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Q: Express the limit as a definite integral on the given interval. lim (4(x")3 – 3x;]Ax, [2, 6] n- 00 i…

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Q: (a) (6) Decide if the following improper integrals are convergent or divergent using Basic…

A: To decide the convergence of the improper integrals.

Q: lim n→∞  n xi ln(1 + xi2) Δx, [0, 2]   i = 1  2   0     dx

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Q: Use integration by parts to evaluate the definite integral: ∫3se^-4s ds with an upper limit of -0.9…

A: A=3∫abse-4sds , solving A where a,b are upper and lower limits as per questionIntegrate by parts…

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.