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Q: Find the solution to the differential equotion that Sotisies the quen inital condiion

A: The differential equation with initial condition is given as

Q: Describe the method used to integrate sin" x cos" x, for m even and n odd.

A: The method to integrate sinm x cosn x when m is even and n is odd. We integrate by substituting the…

Q: Find dy Sinx

A: See the details solution in below

Q: (5) Evaluate the definite intergral [/³ (sec²x+3x)dx. /3

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Q: tan zeecz coS z

A: Integration is the process of finding the anti-derivative function of the given function.…

Q: 5. Evalvate the Intgral S2 cos (2x) - Sin 2x)=

A: To evaluate the integral: ∫2cos22x·sin22x dx Solution: We know that, 1). 2sinθ cosθ=sin2θ 2).…

Q: Evaluate the double integral : (3 – 8z) dz dy

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Q: Directon. tanx 6. Oy= (sinx) Fan a ANS: AN

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Q: Suppose you want to prove that ARST Theorem. If you know that ZR = LX, what else do you need to…

A: In ∆RST  &  ∆XYZ, ∠R≅∠X.

Q: Find the theoretical error bound in approximating SN" sin(x?) dx using Boole's Rule.

A: The theoretical error bound in approximating the integral∫0πsinx2dx using Boole's rule is shown…

Q: tion of all components of v(3) correct to two decimal places.

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Q: Prove: cosh 3x = 4cosh'x- 3 cosh x %3D

A: We will solve the following.

Q: Before integrating, how would you rewrite the integrand of S(x* + 2)² dx?

A: To solve: ∫(x4+2)2dx

Q: Jse differentials to approximate 47. (Express as a rational number.)

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Q: (b) Prove that 1+ cosh x + cosh 2x coth x sinh x + sinh 2x 1+ cosh 2x + cosh 4x dx Hence evaluate…

A: 4b. Given,

Q: 3. Evaluate the improper integral: dx | Tale + 1)'

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Q: 3. Prove that cosh (2x) = cosh²x + sinh²x %3D

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Q: 6. S sin (3x – 1) dx. cos Vi dx. 7. Evaluate th dx. Show yo 8. 3 dx. S (! + 1)(t – 1) dt. 9.

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Q: 3. Prove that coshx – coshy = 2sinh () sinh ().

A: As per honor code we are entitled to solve only 1 question at a time so I am providing you the same.…

Q: 4) coth-lx = .In ( 1+x tanh-11 %3D 2 X-1,

A: i am solving question 4 for other question repost

Q: a 5. Using integration by parts twice, prove that the L (sin ax) %3D s2+ a=

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Q: Use differentials to approximate the value of <2.1.

A: Given  Find the value of 52.1

Q: Find indefinite integral.

A: ∫5lnz+3z dz Put, 5lnz+3=t⇒5·1z+0=dtdz⇒1zdz=dt5

Q: complete solution

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Q: he integra = 3/2 is dz Z-2

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Q: on inteaurron (ii) Determine the general formula for V Pn.

A: Numerical analysis.

Q: integral from -1 to 1 of arccos (y) dy

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Q: By integration find the Fourier transform of Ax)=2r+1 _if þx|<1_and fx)=0 otherwise.

A: According to our company policy, I am supposed to answer only one question at a time. For the rest…

Q: Compute ∫xsin(3x−2)dx.

A: Let the given

Q: 4. y = √esinx + 2 5. y = 4x In 4x 6. xe = sin 5x - sin 3y

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Q: Show that coshr+ sinh a = e and cosh r- sinhr = e. Hence, deduce UTMOU cosh r- sinh z = 1.

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Q: Evaluate In (ax) dx using integration by parts

A: Follow the procedure given below and use simple intergation by parts.

Q: Number 8

A: first find the derivative.

Q: 13. To evaluate f 2costx-1 dx, the integrand can be transformed to 1-sin²x a. [(3cos³x+csc²x)dx b.…

A: Here we have to transformed the given integrand.

Q: Find the particular integ rel of This differential etuatim. (40²+HD+= 2e +8x %3D

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Q: Iterated integrais. 3. ( ye* dx dy Jo Jo

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Q: Use differentials to approximate radical (48.7)

A: Ne need to approximate √48.7 using differentials.

Q: Which is the derivative of y= sin In(5x +2)? * 5 cos In(5x + 2) In 5 5Cos In (5x+2) 5x+2 O Option 3…

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Q: (b) Prove that : - 1) (coshx)2 - (sinhx)2 = 1 ,2) coshx - sinhx = e, 3) (cothx)2 -1= (cschx)2 %3D

A: Use hyperbolic  function

Q: None of These cosh(4t) 7. 2. 7. - sinh( 21) sinh(4t) 7. cosh(21) 7. Sて 1/2 1/2 1/2 1/2

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Q: .find the integral by Gamma fun y(-Iny)5 dy

A: Gamma function is defined as Γ(x)=∫0∞xn-1e-x dx .               Disclaimer: Since you have asked…

Q: 2 = sin5t constitute a fundamenta L

A: Y1=cos5t and y2=sin5t  do not a fundamental set of solutions of differential equations y"+16y=0

Q: (7 – siny)y' = 3x2 + 2x

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Q: What is the Fourier transform of the one-dimensional rect function rect(x) = 1, for |x| |x|…

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Q: Compute the indefinite integral 2. - 4e²² + 6z – 5) 5) dx.

A: We know that integration of ex is ex . And integration of 1/x is lnx. Integration of xn is xn+1/…

Q: Use the composite Simpson's rule with step length h=0.5 to determine 1= [ (2x - - 3x2 + 4x – 1)dx,

A:

Q: The integration expression sin(3In(x)+ 4)cos(3ln(x) + 4)dx must be transformed into using suitable…

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Q: Evaluate the double integral. 5 25- х2 dy dx Jo

A: First, integrate with respect to y