5. 2x sinh+ 3y cosh2) dx -- 3x cosh dy = 0

Q: S In(sin(x))dx

A: Given, I=∫lnsinx dx To evaluate I.

Q: Find dy Sinx

A: See the details solution in below

Q: 4 In estimating | cos(3x)dx using Trapezoidal - 1 and Simpson's rule with n = 6, we can estimate the…

A: Error bound of Trapezoidal rule and Simpson rule for integrating f(x)dx in [a,b] is, ET…

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: 3-S- In(x²+x)-Inx-elnx dx In(ex+1))

A: We will be using the integral formula of log function to solve the above given integral. We can…

Q: 3 In estimating | cos(5x)dx using Trapezoidal and Simpson's rule with n = 8, we can estimate the…

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Q: 1. Ye = cost- sec(at) %3D ans: =-2sin t - asec(at) tan(at)

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Q: 2 9) -sinh? -cosh -dz

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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: In( cosh(7x) + sinh(7x)) + In( cosh(7x) - sinh(7x) ) =

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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…

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Q: If UX = 6 and XY = 6 solve for UV. Round to the nearest %3D %3D hundredth. Y

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Q: Given: 4 2 y = -arctan sinh 3 х — find y' at x = 2 - cosh 1 - y 1 + sinh? 1 %3D cosh 1 y = 1 + sinh…

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Q: 3. Show that sinh a + sinh y = 2 sinh cosh %3D

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Q: Differentiate y = In(cosh x) + 2 cosh x O a. sechx (1 cosh O b. cosh x cosh a 2 O c. sinh x с. cosh…

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Q: 4) What integrals lead naturally to inverse hyperbolic functions?

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Q: 6. Write down an integral that can be solved by using integration by parts with u = sin x and…

A: Write down an integral that can be solved by using integration by parts with u = sin x and…

Q: Flnd * |(sin 5x cos 3x + cos 5x sin 3x) dx cos 8x cos 3x + 3 cos5x – + c 8 + c Option 3 Option 2 cos…

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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: In the indefinite Integral Sin(cosh x + ex). integrand? sinh x + ex cosh x + ex dx, what is the

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Q: In estimating L cos (5x) dx using Trapezoidal and Simpson's rule with n = 8, we can estimate the…

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Q: is 4= Sinh(2sinhix) shaw Hh at %3D 2 (a)

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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: sec Vn du in

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Q: From 0-2 sin(x^2) dx using trapezoidal rule with n=4 as well as midpoint rule with n=4

A: Trapezoidal rule=∫02sin2(x)......(1)As we know that accoding to trapezoidal rule…

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

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Q: 1- -In2 - cosh? () . 2 - cosh(Inx) dx

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

Q: 4) 2²e*dx (Improper Int.)

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Q: 4 + sinh(3x) = 4 cosh(3x).

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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: Find the indefinite integral. Solution in handwritten. 1. secy (tany - sec y ) dy

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Q: I Braluate th FOllowing integralis 3+cos (logqx) dx x sin (loga x )

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Q: 1. Prove: a. S csch x = In b. sech x = 2 Arctan(e*) +c ex+1 2. 2e* tanh e* dx 3. S sinh(5x - 1) dx

A: Given : ∫2extanhexdx Let us consider that : ex=u. Therefore, exdx=du. So, ∫2extanhexdx=2∫tanhu.du .…

Q: 4. Use Trigonometric substitution method to evaluate the integral: dx

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Q: 10. S V9x2 + 64 11. ( sech?(In x) 12. S cosh(5x – 7) dx

A: Given

Q: calculate the integral.

A: Given integral is We will use the following substitution to evaluate the integral

Q: 14. Use a suitable change of variables to determine the indefinite integral. fsin²xcos³ xdx (Hint:…

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Q: What are the new limits of integration if apply the substitution u = 4x + t to the integral / sin…

A: We have to change the limit.

Q: 2 sin x f(x) = 1+2cosx 5. Pvaluated at x = 1 rad

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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: dx =?

A: we have to solve integration

Q: 1 dx. cosh x

A: Rewrite the integral and using substitution method, we calculate the given improper integral.

Q: 7 Show that: sech x dx = Sin¹ (tankx) + ( S note: * & Sim'u = dx 1-U² dx Cam multiply sechx by * you…

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Q: In estimating | cos(4x)dx using Trapezoidal 1 and Simpson's rule with n = 6, we can estimate the…

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Q: integral from 0 to pie over 4 of sin^2 (4x) cos^2 (2x) dx

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Q: Compute cosh(x) and sech(x), assuming sinh(x) = 0.01. cosh(æ) = %3D sech(x)

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Q: 1. Use integration by parts to find (3x – 1) sin x dx.

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

Q: Q3: Find 1. cosh(5x)+ sinh(5x) 2. (sinhx+ coshx)*

A: Given,

Q: (2) find integrals S tanX dx

A: ∫tanxdx here is the direct formula of tanx = ln(cosx) +c