27 dr = iex+ h where a, b> 0. Prove that

Q: evaluate using the appropriate method or combination of methods.

A: Let,

Q: Evaluate the integral, 12 sec(4t) dt 2+3 tan (4t) dt = 2+3 tan (4t)

A:

Q: .rdx dy Prove that (a) (b) (8)

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Q: Q Find the deriva tive using the de fini tion (x)

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Q: Prove that cosh-z = In (z + vz? - 1) %3D

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Q: use the definition prove that s d sinZ %3D Tal

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Q: 2)Evaluate ex dA , Ris bounded by y = x2,y = 1

A: By using Fubini's theorem we solve the given problem.

Q: Evaluate the integral. 10 sec 2(5t) dt J7+2 tan (5t)

A: We have to integrate the  I=∫10 sec2(5t)7+2tan(5t)dt

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

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

Q: OProve that (r=s)Er S is toutology?

A: The objective is to prove that r≡S≡r↔S is a tautology.

Q: Evaluate the integral. "T/3 8 sec 0 tan 8 de IT/4

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Q: By using the substitution method, show that for any positive numbers x and y ry 1 dt = Sdt

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Q: Q3: show that: S yi va -y dy =na² where a is a positive constatnt

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Q: What is ll = ( as")* %3D X= ()3....) where Kn=2"2 %3D

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Q: 3)Evaluate /y² + 1dA , Ris bounded by x = 4 - y² ,x = 0 R

A:

Q: 4. Compute f'dr by using fundamental theorem of integral calculus.

A:

Q: Prove that Cosh [m(t-x) Cosh mh 2mL 2mL

A: The given data is: To prove: emx1+e2mL+e-mx1+e-2mL=coshmL-xcoshmL

Q: If b is dviisible by a (a|b) and b in different than 0 then |a| is less or equal than |b|

A: The given statement means the following.

Q: Anti der ivent ive 2x %3D 37-4

A: Solution

Q: Solve the DE'S ;- with NoA-hamogeneust

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Q: o what does it con s conditionally conv 1. onvergence for at is the radius of approximation of e √2,

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Q: Evaluate the integral. 4 | VE(6 + 2t) dt

A: use distributive property on function and integrate it.

Q: (4 b Prove that 5 foxx dx = K (6-a) using definition of integral, where fø= k [a,b], on

A: Given function is fx=k on a,b. We have to prove that ∫abfxdx=kb−a. Take Left hand side  Use Property…

Q: ove that 1 cosh(tanh) = -1 -1 < r < 1. V1- 2

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Q: s show that: sinhCA+B) = SinhA. cush B + Cosh A. simhB

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Q: Sm Vx dx

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Q: 2.Prove that L (sinwt) %3D s2+w?

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Q: Prove using the IVT. ex + In x = 0 has a solution.

A: IVT: If f is continuous on the closed interval [a, b], f(a) ≠ f(b) and k is any number between f(a)…

Q: Use the difinition of error function Prove that: 5(1/₂/2) = 5T let: ere (x) = 33/3324 dt

A:

Q: 11. Prove that tanh y du = In cosh u + C

A: The integration of the integral is tanhu.

Q: 28. IfI:zxzr = 0, ris a. positive b. negative с. zero d. impossible to determine from the…

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

Q: 49 Vã.) х dx х. Let u = х — 9 36

A: Given:

Q: Show for Re(z) > 1 ex – 1 dr = T(z)5(2). et – 1

A:

Q: 7. Prove that if v >-1/2 ; p) = L{xvJ, (; = xı-at-a) H

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Q: (z In z + 5)dz

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Q: Compute for the value of constant (C) by solving the given DE using integrable combination. Let x=2,…

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Q: J sec° (10t) tan“ (10r) dt 4 10.

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Q: 4. Evaluate de J V20 – 02

A: we have I=∫dθ2θ-θ2 make the complete square of the denominator i.e. 1-(θ-1)2 now substitute…

Q: 27 Use the Fundamental Theorem of Calculus to evaluate S (Vx2 -) dx. 8.

A:

Q: Evaluate the integral fff, xyzdV,where: E = {(x, y, z)|–1 <x< 1,0< ys 2,1 szs 2}

A:

Q: Compute for the value of constant (C) by solving the given DE using integrable combination. Let x=1,…

A: Use by exact form

Q: 4 da 25 + z? Integrate:

A:

Q: Show that {zn}nEN is Cauchy, where z, = sint dt. 1+t

A: Sol

Q: pes of animals are treated by at least on r. Scott, and Dr. Baker)?

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Q: Use Simpson's Rule with n = 4 to evaluate [² (t³ + t) dt

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Q: Evaluate the improper intergal 1 -00 dx using the residue (x² + 16)3 theorem. 00 2

A:

Q: Q2-Prove that = va* – x² ify= ()sin () + () va² - x* = va² – x* if y = (;")sin*+ (4) + () Va² - x²

A: