Determine whether the improper conrergent divergent. or It sin (x) 8. x²+1 dx

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A: we have to solve the integral

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A: The given integral is ∫sin23xcos53xdx. We have to evaluate the given integral.

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A: We will use the definition of the derivative  Here f(x)=cos(x) So,

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A:

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A:

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A:

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A: To Evaluate the integral

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A:

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A: Given : ∫(sin x/√2 - cos2 x) dx     ....(1)   Let cos x = t   Differentiating both sides w.r.t. x -…

Q: -2,2] R, then show that the function sin for x 0, f(x) = for x 0, aly continuous.

A: There is no such introduction for the solution.I have explained it within the solution.Please go…

Q: 2 Find def differentiêt equatcn of: -I(082 Siny %3D

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A:

Q: ue of J. Note that the lows

A: Given ∇.V=1r2∂∂rr2vr+1rsinθ∂θ∂∂θsinθvθ+1rsinθ∂vϕ∂ϕ

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A:

Q: Hico/ prove Thall Cosh2: - 2 tañ z Sinhz: 1+2 Tanhiz =

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

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Q: = tanh (2x) Use the definition of the hyperbolic functions to prove the identity 1– cosh?(2x)

A: 1-1cosh22xUse the Hyperbolic identity:  1coshx=sechx=1-sech22xUse the Hyperbolic identity:…

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Q: Prove that: sin z = sin x cosh y +j cos x sinh y

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

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A: Given : y=secx To prove : dydx=secxtanx using first principle. Proof : By First principle, we have…

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A: Given ∫01∫sin-1yπ2sec2cosxdxdy

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A: To evaluate the integral:

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A: Here we have to use the given identities to prove.

Q: dx хе

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Q: 3 dx 23.

A: Given:

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A: We know that cosh(θ) = eθ+e-θ2sinh(θ) = eθ-e-θ2

Q: Find the sine transform of and deduce that TUX e 1 tanh (p/2). |(2x) F, (cosech rx) = %3D

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A: NOTE: Refresh your page if you can't see any equations. . ..............(1) substitute  take…

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Q: Q4) Prove that dx 1+ 2 sinx || In √3 Χ tan tan x + 2 -√√3 +2 + √√3

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A: Given : Integration of X2sin(X3)dx