The set of all values of p which makes the integral x* dx is divergent is a) (-1, 0) b) (-n,-1) c) (-1,00) d) (-0,-1] e) None of all

Q: Show that limit t  appraoaches infinity  integral -t  to t  x dx =0

A: To prove:

Q: Evaluate the Integral iF the funthun X = = XSin (xy) ニ over the vecfongulor region R- [0,1][1, 2]

A:

Q: Suppose that f is integrable on [-4, 7]. If the average of f on the interval [-4, 7] is 4.25, fin 4…

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Q: 1. Give an example of a bounded function which is not Riemann integrable over (0,1).

A: According to experts guidelines of bartleby i have solve first question so repost for further…

Q: 3. (a) Set up the integral for the are length of the parabola y=2x* from (0,0) to (1,2). (b) Set up…

A: As per Bartleby guidelines for more than one question asked only one is to be answered please upload…

Q: 5. Use the binomial expansion and Cauchy's Integral Theorem to evaluate ( с 2n dz Z + -/-/-) where C…

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Q: What is the resulting integrable form of evx+I x+1

A: We have to find value of given Integral.

Q: Compute ₁₁x dx using the concept of integral as limit of sums.

A: The given integral is ∫-11xdx use the properties of integral: ∫abf(x)dx=∫acf(x)dx+∫cbf(x)dx, where…

Q: Let f,g:[a, b]-X are Riemann integrable , f-g is Riemann integrable.

A: Let f,g:a,b→R are Riemann integrable.To prove that f-g is Riemann integrable.

Q: Use Theorem 5.2 to prove directly that f(x) = x is integrable on [0, 1]. Find the integral of f by…

A: The given function is  f(x)=x    if x is rational0     if x is irrational Here, we have vx-0>0…

Q: I, FIND HE NET AREA OF fos) - Zx and gx)= O FROM [-3,3]

A: Given : Functions f(x) = 2x and g(x) = 0   To find : Net area of f(x) and g(x) from [-3,3]?

Q: Let f,g: [a,b]-R are Riemann integrable , f-g is Riemann integrable. ylgn

A: True.

Q: 5) Evaluate the integral.cusc c for the constan6 of integrafion) 2(ean cx) +6an cx>) dx

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Q: 2. Sketch the region of integration of the given integral Q in #1. Set up Q by reversing its order…

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Q: Compute the definite integral as the limit of Riemann sums. .2 3) (x2 + x + 1) dx

A: Definite integral

Q: 3. If f : [a,b] → R is a bounded function such that f(x) = 0 except for x in {c1, C2, .., Cn} in [a,…

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Q: Compute the indicated integrals. [ In°(x)(In*(z) – 5)ª dr. (Hint: In°(x) = In²(x) · In°(x)...) (a)…

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Q: Show that is integrable on [0, 1]. f(x) = {1. 0, +√√xsin(1/x6), x‡0 X 0

A: Given that f(x) = 1 + x sin 1x6,x≠00,x=0 To prove that, f(x) is integrable on [0, 1]

Q: . Compute the line integral of E from B(0,0,0) to A(2,1,3) if E = -4xya, – (4y + 2x2)a, + 8zaz. Use…

A: The line integral of vector field E→ along curve C is ∫C   E→.dr=∫abE→(r→(t).r→'(t)dt  where r(t)→…

Q: Define Riemann integral in R^3

A: Partitions of an interval-   The partition of an interval [a, b] is a finite set P of points…

Q: 2. Prove or disprove that Z, xZ, is integral domain.

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Q: Show that I¿(f) = 1, and conclude that f is integrable on

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Q: 1 Evaluate the improper integral or show that it is divergent. x In x

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Q: Сompute f dx, where f(x)=|x|.

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Q: Prove that (Z(sqrt(2)), +, ×) is an integral domain.

A: We know that , ℤ2 = a + b2 / a , b∈ℤ . Clearly , ℤ2 forms a ring. We know that , a commutative ring…

Q: In (a le) secx ((2- sec²x) " sec (3А - x) to be integrable using the formula What should be the…

A:

Q: Calculate the integral: /3 arctan(x) dr a) O 3x arctan x – In(1 + x²) + C b) O3 In | arccos x| + C…

A: we will apply the integration by parts rule: ∫(u·v) dx=u∫v dx−∫u'∫v dxdx And we also use…

Q: (10) Is the line integral ſc f(2)dz always vanishing for all holomorphic functions f on ID, where C…

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Q: 2 5 6z³ -8z¹+2z² 4 Z dz

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Q: If f: [a, b] - R is bounded and has only a finit number of discontinuous points, then f is Riemann…

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Q: Determine the convergence of the integral tan r dx J; (In(cos x))²

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Q: Riemann-integrable

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Q: Evaluate the line integral S. 4x²ds, where C is the line segment from (-2, –1) to (0,–1) followed by…

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Q: Compute the integral of f(x) = 0.3 – 2x² + 40x³ from a = 0 to b = 0.8 using i. Trapezoidal Rule with…

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Q: Show that f(x) = x² is integrable on [a,b].

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Q: 3. Evaluate JIJ 62² dV where G is bounded by x + 2y + 4z = 8 in the first octant.

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Q: Show that if f is Riemann integrable on [a,b] and f(x) ≥ 0 for all x ∈ [a,b], then

A: A bounded function on a compact interval [a, b] is Riemann integrable if and only if it is…

Q: Only piecewise continuous functions f(x) on every finite interval (0, ∞) such that F(x)| dxis…

A: The given statement is false.

Q: The double integral; ) dA Sin(x2+y², (4+X2+42)- 2. is it convergert this regon; Conu in {x20,y>OS

A: Now, we need to verify the convergence of the above integral.

Q: Evaluate the integral; f, Ni-1, tsin(at)) dt

A: Evaluate the definite integrals  in the following  way:-

Q: Provide a homotopic squared parameterization of side one o_1= [-1,1] x [-1,1], other than this, and…

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Q: Show that f is not Riemann integrable on [0,2].

A: This is a question of R-integration and measure theory.

Q: In(In z) | (In z)* ( +

A: The given integration can be written as:

Q: Determine the convergence of the integral tan x UTM &UT dx. (In(cos x))² COS X

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Q: 17. Iff is bounded and integrable on [a, bl, then IfI is also bounded and integrable on [a, b] and f…

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Q: or state that it diverges. Show all work. Evaluate the given integral 5 dx 7. Jo x-3

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Q: continuous on ( UOUS O

A: Given function is: fx=3x+6a  ;  if x<-33ax-7b   ;   if-3≤x≤3x-12b   ;    if 3<x We have to…

Q: Calculate the Riemann Sum for the integral using n= 4. x-dx x*dx -4

A:

Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products. 

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.