Evaluate the integral / f(x) dx, where -1 -x - 1 if - 1 < x < 0 if 0 < x < 1 f(x) = l-VI- x²

Q: f r cos(x')dx

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Q: Express the limit as a definite integral on the given interval. n lim X; In(2 + x;) Ax, [0, 4] i = 1…

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Q: 1. Use the definition of the definite integral as the limit of a Riemann sum to evaluate - 4)² dx.

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Suppose f is an odd continuous function whose mean value (with respect to integral) on the interval…

A: We have to use property of odd function here.

Q: x sin-'(x²) d.x V1– x4

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Q: x³ + 2x² + 3 4/9 dx 3x6 + 17x10 + 10x12 8°

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Q: Suppose f is an odd continuous function whose mean value (with respect to integral) on the interval…

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Q: Suppose f is continuous on the closed interval l-1,3] if Fis an antiderivative of f, which of the…

A: We have given that f is continuous on the closed interval [-1,3] . If F is an antiderivative of f .

Q: The area above the x-axis, below the graph of f(x) = between x=0 and x=2 is the limit of 1+z which…

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Q: The integral in this exercise converges. Evaluate the integral without using a table. e-14x dx - 14x…

A: We have slove the integral

Q: Find the values of  p for which the integral convergesand evaluate the integral for those values of…

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Q: Suppose a definite integral has lower and upper bounds as follows. 1 1 f(x)dr <3 12 8 If 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: In(x) Differentiate the function F(æ) | cos(e') dt (for x>0). %3D 1/r Show and justify your work.…

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Q: Let f and g be continuous on the closed interval L0,5]. suppose that J s(x)dx=A, / f(x) dr=B, The…

A: Here, to evaluate: ∫35(f(x)-g(x)) dx

Q: 2. Express each definite integral as a limit using summation notation: In x dx = L(8x – x²)dx =

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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 whether the integral is convergent or divergent. 31 2 + e-x…

A: Definition used -               Comparison test for integrals-                   If  0≤g(x)≤f(x)…

Q: Use the definition of the definite integral a sum to evaluate | (2 – 3r)² dxr. as a limit of

A: Given:           I=∫-112-3x2dx To Find I using definite integral as a limit of sum:

Q: 5. Suppose fand g are continuous functions and that: f(x)dx=-4, f(x) f(x)dx=6 and 8(x)dx=8 use the…

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Q: 2. Using the definition of the definite integral as a limit of the Riemann sum, evaluate S, 3x + 1…

A: Since you have posted multiple question in this question so I have solved first question as per our…

Q: The functions f and g are integrable and f(x)dx 2. f(x)dx 4, and g(x)dx= -3. Find the values of the…

A: Given, ∫24fx dx=−2,∫27fx dx=4 and ∫27gx dx=−3Concept used:1. ∫aafx dx=02.  ∫abfx dx=−∫bafx…

Q: The integral of ƒ In(ln(x))dx can not be expressed as a finite sum of functions. What do we call…

A: It is called as non elementary integral

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

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Q: Determine whether the improper integral converges and, if so, evaluate it.

A: ∫56dxx-532 On integrating, we get ∫56dxx-532=∫56x-5-32…

Q: x cos x - sin x - dx x2 x sin x dx roo dx |(x* + 1)²

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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: Define the function f(x) by 1 if x = 0, f(x) = sin x/x if 0 < x (Note: We define f(0) = 1 so that f…

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Q: Assume an improper integral produces the given limit. Evaluate. 2x e 1 - lim x-0 5x

A: We need to find , limx→0 e2x - 15x limx→0 e2x - 15x =15 limx→0 e2x - 1x Now , this is 00 form, We…

Q: Express the limit as a definite integral on the given interval. lim. x, In(2 + x?) Ax, [2, 4] n- 00…

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Q: Evaluate the following definite integral using partial fra x- 1 3 x' + x *

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Q: 10:04 A Write the following improper integral as a limit. x-3x' In(x)-1 dx x (x-1) Determine whether…

A: The given improper integral is ∫1ex3-3x3lnx-1xx3-12dx

Q: Use the form of the definition of the integral given in the theorem to evaluate the integral. 24 (1…

A: Answer

Q: 1 dx (r-2)2 а.

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Q: 1. Use the definition of the definite integral as the limit of a sum to evaluate (4.x – 2²) dx.

A: The given problem can be solved as-

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

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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 following limit of sums as a definite integral. sin(1 + () lim i=1 1 sin(1 + x2) dx x…

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Q: Given a decreasing concave up function f(x) on the interval [2, 5] with f(2)=10, f(5)=3, f'(2) =-4,…

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Q: determine whether the improper integral converges and, if so, evaluate it

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Q: You will be investigating the following integral: + 28x)dx Evaluate the above integral by setting up…

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Q: Express the limit as a definite integral on the given interval. 5 V 3x; + (x;) Ax, [2, 3] * lim n →…

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

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Q: Suppose fis continuous on the closed interval l-1,3]. if Fis an antiderivative of f, which of the…

A: We to check correct option by antiderivative property

Q: Consider the following. -X dx 8e 1 Find the indefinite integral and set up the limit that will be…

A: Here given  It an indefinite integral. Now set up it into limit form as

Q: 14. Let f(x) = 4.x3 + 6x2 + 3. (a) Use a right-hand Riemann sum to approximate the definite integral…

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Q: Evaluate this integral I = ∫ x^4 (ln x)^2 dx and then determine if this statement is true or false,…

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Q: Use the Comparison Theorem to determine whetherthe integral is convergent or divergent integral 1…

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Q: a) Determine if the following integrals are convergent or divergent: sin? (x) x +1 dx dx Vr4 – x -

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