3. |2" – 8| dx sinh? (e-) 4. dx e cosh(e-*)

Q: Find the indefinite integral ∫sin 5x sin 4x dx

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Q: 9. cosh x + sinh x= e* %3D

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Q: 9. cosh x + sinh x = e* %3D

A: To Prove,                cosh x+sinh x=ex

Q: (b) Prove that : - 1) (coshx)2 – (sinhx)2 = 1 ,2) coshx- sinhx = e-*, 3) (cothx)? -1= (cschx)?

A: Given that  The following

Q: Using Newton's method, the approximation of the root x of f(x) = 2 – x² – co within 10 starting with…

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Q: 53. Find the value of 1 dx using weddle’s rule. 1+x?

A: Weddle's law is a formula for solving numerical integration.

Q: In estimating cos(3x)dx using Trapezoidal and Simpson's rule with n = 8, we can estimate the error 1…

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Q: Use Simpson's rule with n = 4 to approximate cos(x) dx 1

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Q: use this to evaluate /x*sin (2x)dx

A: Integrating using by parts...

Q: sinh In(2+2x) dx? x+1

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Q: (7) coshx + sinh x = e* %3D

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Q: By using the exponential definitions of sinh and cosh. show that cosh (t) - sinh (t)

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Q: Show that coshxt sinhx= ex and coshx- SinhX = e-x, Hen ce deduce cosh?x- Sinh?X=|

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Q: .Find a reduction formula for ea* sin" x dx. Hence evaluate e* sin x dx. 3

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Q: aluate 9/ sin(x) cos(x) dx by four methods.

A: Here we want to perform the given integral according to each of the methods mentioned.

Q: Verify the identity sinh x + cosh x = ex

A: To prove the identity

Q: In estimating cos(3x)dx using Trapezoidal and Simpson's rule with n = 4, we can estimate the error…

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Q: Prove the identity. cosh(x) + sinh(x) = e* cosh(x) + sinh(x)

A: The solution of the problem is given in the next step.

Q: 4. Show that sinx can be approximated by x-x³/6 within 0.01 on the interval [-1,1].

A: see my solution

Q: S x2tan (x³)dx

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Q: Find the indefinite integral. sin(9x) sin(2x) dx (Hint: See the hint for Exercise 50 in Section…

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Q: Prove the identity sinh 2x = 2 sinh x cosh x

A: Prove that: sinh 2x = 2 sinh x cosh x

Q: Evaluate 1 ei sin x cosx dx using Simpson rule with h = 20

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Q: 6) Using gamma function, evaluate So 6 хе 2x dx

A: Introduction: Gamma function is an integral function that is defined through an integration. The…

Q: (A) Prove that: cosh x + sinh x = e*

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Q: 5. If cosh 2x then the positive value of 4 sinh 2r is

A: Here we will use the relationship betweencosh2x and sinh2x to find the value of sinh2x from the…

Q: Verify the identity cosh 2x = cosh2 x + sinh2 x

A: we have to verify the identity: cosh(2x)=cosh2x+sinh2x   L.H.S: cosh2x as we know that coshx=ex+e-x2…

Q: Use Simpson's rule with n = 4 to approximate cos(r) -dx Keep at least 2 decimal places accuracy in…

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Q: 7. To evaluate f-cos X-1 dx, the integrand can be transformed to? 1-sin? x

A: Follow the procedure given below.

Q: sin 3xdx Evaluate: S 4+cos?3x

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Q: In estimating | cos(3x)dx using Trapezoidal and Simpson's rule with n = 8, we can estimate the error…

A: We have to find the error in trapezoidal and Simpson rule .

Q: sinh4x cosh 4x dx can best be evaluated by General Power Formula. A True False

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Q: The equation xsin x + cos x =1.015 has a positive root a close to zero. Use small-ar approximations…

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Q: sin $3xcos 3x dx

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Q: The integral S sine de 1+ cose sec²0 de 1+ tan cose de 1-sine sece tane de sece-1 S x dx x²+√√x²-1-1…

A: dsecθdθ= sec θ.tan θ

Q: 3. sin 8x cos 8x dx s 2x sin 2x dx cos

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Q: In estimating cos(5x)dx using Trapezoidal and Simpson's rule with n = 6, we can estimate the error 1…

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

Q: Consider sin °x cos2x dx. f we let 4=cos x, the integrand can be transformed to

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Q: Use Simpson's rule with n = 6 to approximate cos(a) dx Keep at least 2 decimal places accuracy in…

A: The solution is given below in the next step:

Q: cos (5x)cos (3x) dx cosh' (In x) sinh (In x) (A) (8) - (C) 0 (D) 2 1

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Q: 3. Use Simpson's rule to calculate x² sin x dx to within 2 × 10-5 of the exact value.

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Q: Prove the identity (cosh x + sinh x) n  = cosh n  x + sinh nx

A: Consider the given L.H.S of the given identity coshx+sinhhxn

Q: 4. Evaluate sin (44°) + + COS (29°) using differentials. Refer to special triangles.

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Q: do sin 0 – cos 0 cos 0

A: The given integral is ∫dθsinθ-cosθ

Q: Use integration by parts to verify the reduction formula.

A: We have to verify the reduction formula using integration by parts, ∫cosn x dx=cosn-1 x sin…

Q: 10.y = Arc cot (sinh3x) 11. y = cosh?4x - cos 12. y = In (sinh4x) cosh8x +x² 2

A: To find dy/dx: 10.y = arc cot ( sinh3x ) dy/dx = [1/(1+sinh23x) ]( cosh3x) 3  = (3 cosh3x) /…

Q: 2. 1 Given: cosh x==(e* + e*), =(e* - e**), use these sinh x = definitions to show that cosh²x-sinh2…

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Q: In estimating : cos(4x)dx using Trapezoidal and Simpson's rule with n = 4, we can estimate the error…

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Q: I. Verify the following identities: 1. cosh x- sinh x = e* 2. sinh(-x) = –sinh x 3. cosh(-x) = cosh…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…