In=5 dx Sin^ (x) ( ategrate by parts for findu the Yreduction form (11) by using (i) find In and five decima dx Sin4(x) → round the value places.

Q: Find y′ if y = tanh−1(sinh x2).

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Q: (sech°x)/1+ sin? if y = dx dy Find tanh°x

A: Given:-       To find:- dy/dx

Q: 10) y = xtanx + sin-ly

A: according to guidelines we should able to do only one question at a time #10

Q: Solve 2 sinh(x)– cosh(x)= 5 by using the definition of the hyperbolic functions.

A: We know thatsinhθ=eθ-e-θ2coshθ=eθ+e-θ2

Q: Evaluate S sinh x cosh x dx by introducing u-sinh x

A: Given that: ∫sinhx.coshx.dx

Q: d sinh x) = cosh x dx

A: By using hyperbolic functions definition, sinhx =ex-e-x2   and coshx =ex+e-x2

Q: Integrate O sinh 2x dx

A:

Q: |Calculate the indefinite integral / sec (0) tan(@)d0 using two different u-substitutions. Explain…

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Q: √xA)• dS over the surface of a hemispherical bowl of radius 2 and its circular rim if A = 3 sin(-)â,

A: Please see the attachment

Q: solve for dy/dx :  arcsin (x/y) + arccos(y/x) = 5

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Q: S) - aresin 2. 2 arcsin 2. is constant for 0sxs 4.

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Q: Verify Eq. (2): cosh 2 x - sinh2 x = l.

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Q: In estimating cos(5x)dx using Trapezoidal and Simpson's rule with n = 4, we can estimate the error…

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Q: Integrate  dy/dx sinx=1

A: We know, ddxcosec x = -cosec x·cot x ddxcot x=-cosec2x ddx(cosec x-cot x)=-cosec x·cot x + cosec2x…

Q: S sin x In(cos x) dx X

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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: Show that d /dx  arctan ( tanh x ) = sech 2x

A: We have to show that ddx(tan-1tanhx)=sech2x

Q: find dy / dx for Hhe tellowing in (sec EX) In (cosp?}

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Q: dy Find by implicit differentiation. dz 3+ 5z = sin(ry) dy

A: We can find the answer using implicit differentiation as below.

Q: 4. Evaluate: a) 4 (earctan x)dx o dx b)음 arctan x dx # earctant dt

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: Find the surface area of revolution of 7 cos(5θ ) between - π/10 and  π/10, about the x-axis using…

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Q: If y- sinhx then prove that dy dx

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Q: Find , if y = x sinh x - cosh x %3D dx

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Q: Problem dy Use implicit differentiation to find dx Vx+ y² = siny

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Q: If tanh(x) = 24, find the values of the other hyperbolic functions at x. sinh(x) %3D cosh(x) coth(x)…

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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: i) S'(2x – 1)* dx (In x)2 j) fth dx 7 k) S (1-- -)dx (x2+1) 1) S(1+ tan² x) dx

A: I am attaching image so that you understand each and every step.

Q: 2. Jx sinh x2 dx

A: ∫x sinh x2 dx

Q: sin“ (x)dx 4

A:

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: Sinhx cosy dx = coshx siny dy

A:

Q: dy =Cos x Sinx cotX 8-

A: As we know that; The standard form of the linear differential equation; dydx+Py=Q Where P & Q is…

Q: dy Find by implicit differentiation dx 4 + 5x = sin(xy*) dy dx II

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Q: show that d/dx arctan (tanhx) = sech (2x)

A: On differentiation, we get

Q: Find the length of the curve defined by 2 y = 5 ln 5 from x = 7 to x = 9.

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Q: 1. [cosh(x)] = sinh(x) dx

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Find dy/dx by implicit differentiation. 5y sin(x2) = 9x sin(y2)

A: Given :  5y sin (x2) = 9x sin (y2)

Q: tanh 2x In (cosh 2x)dx

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Q: Integrate f sinh 2x dx

A: In this question we have to find Integration.

Q: Arc lenght of Curue y=ln(sinx) at intervol I sxS Ę

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: dy dx by implicit differentiation. 9. Find sinx +Scos 3y = 4

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Q: Find dy/dx by implicit differentiation   4Sin (x2) =x Sin (y2)

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Q: X= sin 2tS In %3D Find dw 2- Cost

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Q: 4) S tanx dx cosxv1+secx 5) S(1- u)Vūdu

A: (4)  First we integrate this ∫tanxcosx1+secxdx

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: d. tion to prove that (cscx) dx = – CSC X COt x. 86. Use the quotient rule and the derivatives of…

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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: Se Sin (3x) dx by Improper htegrations.

A: use improper integral

Q: Find when 4= SINX Thuen dy (sinx) (ar f(s wheve for 0<x< M2 tanx taux a=?

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.