Let ECR be measurable. Prove that L'(E)n L°(E) C L*(E).

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

A: To prove:

Q: cos®xdx CoS Xx, 0.

A: We have to evaluate the integral.

Q: The integral of the right hand member of the first order LDE +2r cote = sin2 e is: de A sin*e +C 2 2…

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Q: 1 Prove that 3 dx s VI VI

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Q: 59. Show that for any number a > 1 -Ina In x dx + e dy = a In a,

A: Given: ∫1alnxdx+∫0lnaeydy=alna

Q: Evaluate the iterated integral: a S " cos(2) dy dar.

A: Given that the double integral

Q: Prove that X Pn dx %3D

A: Recurrence relation.  Partial fraction.

Q: Use the Fundamental Theorem of Calculus to evaluate (if it exists) -5t- dt. If the integral does not…

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Q: Prove That:- o sinhz= loy (Z+lz*+l )

A: To prove, sinh-1z=logz+z2+1     Lets consider, y=sinh-1z…

Q: Calculate the area of the inner loop of r = √3 − 2 cos θ.

A: To Find: Area of the inner loop of r.

Q: Use the fundamental theorem of calculus part 2 to evaluate the 3 integral: (8 sin x) dx. Noto: Round…

A: Our Aim is to evaluate the integral given below:-∫π/4π/3 (8 sin x) dx -(i) using Fundamental Theorem…

Q: Evaluate the integral. ∫0 π/4 tan4 t dt

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Q: Find the Fourier integral of f(x) = e-k* when x>0 and f(-x) = f(x), hence prove that cos(wx) dw w…

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Q: If m(E) = 0, show that any function f: E → Ris Lebesgue integrable and Se f = 0.

A: Given, mE=0 So, a measurable function f:E→ℝ is said to be Lebesgue integrable  (or simply inferable)…

Q: Evaluate the integral, if it exists.

A: Given: ∫-π4π4t4 tant2+costdt

Q: | cos' x| dx 3

A:

Q: Evaluate the iterated integral cos(s') dt a

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Q: Evaluate the integral. (11 - t)/e dt

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Q: OI ) is Continuous on at and fo-0 then afinite inderval [e, Sup Ifol

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Q: Prove that for all r € [1, 00), – sinh (- |cosh-(x)|) = vVI² – 1.

A: We know that: Cosh-1x=logex+x2-1  and  Sinhx=ex-e-x2. And, Sinh-x=-Sinhx. Therefore,…

Q: Consider the definite integral. (8x- – 1) e*x²-x dx Let u = 4x2 - x. Use the substitution method to…

A: Answer and explanation is given below

Q: Evaluate the integral. ∫0 π Cos42t   dt

A: Given: I=∫0πcos42tdt we know that 1+cos2θ=2cos2θ similarly, cos22t=1+cos4t2 now substituting value…

Q: The integral of the right hand member of the first order LDE +2r cote = sin20 is: de -cos4e + C A 2…

A:

Q: At the point of discontinuity on (0, co), the Fourier Cosine integral corverges to: f(x+) – f(x¯)]…

A: We have to solve given problem:

Q: Evaluate the integral S CO|CT CT | CO CT /Co NIC 8 dx using the two-point Gaussian quadrature rule.…

A: We have to evaluate the integral ∫−22816+x4dx using the two-point Gaussian quadrature rule. Here,…

Q: Prove that coshz =log ztv= {Hint : cosh z =e} 2.

A: Use the hint and prove this.

Q: Suppose f is Reimann integrable on [a,b]. If f (x)< 0 for all x E [a, b], then S f(x)dx

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Q: Find the integration of S ecosx dx using Trapezoidal and Simpson's Rules

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Q: Compute f dx, where f(x)=|x |

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Q: Evaluate the integral f 2x ¡dx using the two-point Gaussian quadrature rule. 16 \\frac{2}{3}\)

A: Given integral is ∫−222x216+x4dx. We have to evaluate the given integral using the two-point…

Q: Evaluate the following integral JI (1 – (x + y))dA where T is the triangle with vertices (0, 0), (1,…

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Q: Evaluate the following indefinite integral. dt = +C

A: topic - indefinite integral

Q: Compute algebraically the resultant of the following complanar displacements: 100 N at 30°, 141.4 N…

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Q: Evaluate the definite integral. sin(3t)dt Preview kl3

A:

Q: Use symmetry to evaluate the followingintegrals.

A: Given: An integral ∫-22x2+x3dx By symmetry an integral of form ∫-aafxdx can be written as…

Q: Use Wallis’s Formulas to evaluate the integral.

A: Wallis's formula for integration for even n: ∫0π/2cosnx dx=12·34… n-1nπ2

Q: The integral S x dx x²+√√x²-1-1 can be transformed to which of the following using trigonometric…

A: Please follow the next step.

Q: dy is then da In a If y = cosh r

A:

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 the following line integral is path independent an (3, 2) S cosh(+ X (0,0) (8xdx+6ydy)

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Q: Evaluate the integral: f/2² sin (-) dt du ,2

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Q: Evaluate the integral.   ∫01 t cosh t dt

A: Given: ∫01tcoshtdt

Q: Evaluate the improper intergal 1 dx using the residue (x² + 1)3 theorem.

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Q: Evaluate the following definite integral. sec2 dt /14

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Q: Evaluate Poisson Integral: In(1-2a cos(x) + a²) dx ,a.) [a| 1,

A: To evaluate Poisson's integral: ∫0πln1-2αcos(x)+α2dx  a)α&lt;1 b)α&gt;1

Q: If In |(In x)" dx, show that In = x(In x)" – n.Ip-1- Hence find nx)* dx.

A: I am going to prove the given identity by using integration by parts and then use this identity to…

Q: determine the area inside of the inner loop of the limaçon r = 2 cos 0 – 1.

A: We have to find area of r= 2cos(theta)-1

Q: Prove,J w' Sin wx du %3D COSZ 2

A: