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

Q: Find the arc length of y = 3x – 1 on 0 < x < 4. < 4. -

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Q: ye(2y*) dy

A: Given the integral I=∫ye2y2dy     ....(1)

Q: Use the trapezoidal rule with n = 4 to approximate cos(x) dx finel

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Q: Plot along with its tangent r = -6ecos0 + 8 cos 40 in %3D 4

A: We knowx = rcosθy = rsinθGiven: r = -6ecosθ+8cos4θ                     Where θ∈0,2π     Hence, x =…

Q: Calculate the arc length of y = ((72x)/2 – (72x)2) over the interval [2,8].

A: For Y=F(x) , a≤x≤blength of the curve = ∫ab1+dydx2 , dx                        or                arc…

Q: Evaluate 1cos ax dx and 1sin ax dx, where a is a constant.

A: We know that, ∫cosθdθ=sinθ+C           ⋯⋯1∫sinθdθ=-cosθ+C     ⋯⋯2 (a) We have, I=∫cosaxdx Let us…

Q: Find dy Y= 5In CI+x") 4 dy'=?

A: The solution are next step..

Q: | sin(6y) sin(8y) dy.

A: we have to solve the integral

Q: Calculate the arc length of y = 8x + 1 over the interval (0, 10].

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Q: The approximation of I tanx dx using composite Simpson's rule with n=5 is: = None of the choices

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Q: Let 5 sin æ + 6 cos y = 6. dy dx d?y dx?

A: 5 sinx +6 cosy = 6  Differentiating w.r.t x,  5 cosx +6 (-siny) dy/dx = 0  dy/dx = 5cosx/(6siny)

Q: satisfies thé équation:y + 13y - Show that y=e Sin 3x

A: Topic = Derivative

Q: Differentiate implicitly to find dx Зху + 5 3 0 dy %3D dx

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Q: Evaluate 112x C: arc on y = x5/2 from (0, 0) to (4, 32) (2x - y) dx + (x + 3y) dy.

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Q: Integrate cot(r) In(sin(x))dx.

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Q: Integrate by parts: Je*sinx dx So

A: The the given integral is, ∫exsinxdx Assume I=∫exsinxdx.

Q: 2 Find the arc length for y = 3x3 on [1, 8]

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Q: Calculate the length of arc of y = 2x/² for 0≤x≤1

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Q: Use the trapezoidal rule withn= 4 to approximate %3D cos(x) COS

A: Given: n=4 and ∫15cos(x)xdxwe know that trapezoidal rule for approximating ∫abf(x)dxis given…

Q: b) Differentiate (Cosx)Stnx with respect to (Tanx)Secx

A: We have to differentiate cos xsin x with respect to tan xsec x

Q: 9– x² -dx

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

Q: B. Use the trapezium rule with 6 ordinates to estimate fe* dx correct to two decimal places.

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Q: (b)/ Use the Trapezoidal Rule with n = 4 to estimate (x' + 1)dx.

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Q: Find the arc length of y 4x – 1 on 0 < x < 2. -

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Q: Use the trapezoidal rule with n = 2 to approximate the value of sin(x²)dx. Round your answer to four…

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Q: Use the composite trapezoidal rule with the step length h = 0.1 to evaluate sin x -dx, in six…

A:

Q: Find dy/dx in terms of x and y if arcsin(x'y) = xy". dy dx Submit

A:

Q: Differentiate: y = v25 – 22 – 5 arccos() 5+2 O y = O y = %3D Oy =

A: derivative

Q: Show that the antiderivatives are equivalent.                                                     ∫…

A: To show that ∫3x21-x6dx = arc sin x3+C Substitute  u = x3. Then                  dudx=3x2du  =3x2dx…

Q: 22. Use the Trapezoidal Rule with n = 4 to approximate 1 (x− 1)² dx

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Q: Integrate sin" uelor (cosu) . Where n=540

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Q: Use the trapezium rule to find [2" dx taking ordinates with interval 0.25, in three decimal places.

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Q: Prove d [sin-! lu(x))]= I dx dulx) %3D NI- Culx)]? dx

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Q: I = f, (sinhz + 1)dz. %3D

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Q: use Eq. (8) to find dy/dx at the given point.  (sin 2θ , cos 3θ ), θ = π/6

A: Solution:Given   (sin2θ, cos3θ),     θ=π6To find dydxFormula:ddxsin θ=cosθddxcos θ=-sin θ

Q: 4) limo Arcstnxx to

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Q: (a) --y = 2x?y, y(1) = 1 dy dx

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Q: Evaluate the integral cot 2x dx cot2 2x - 15 -금사 csc 2x +C A Arcsec 4 B -In/cot 2x + cot? 2x – 15|+C…

A: Here, the given integral is: I=∫cot 2xcot22x-15dx

Q: Let 3 sin x + 7 cos y = 3. dy %3D dx d²y dx?

A:

Q: The approximation of I tanx dx using composite Simpson's rule with n=5 is:

A:

Q: sE de = 6 - +- + arctan( )) +c %3D 1+ Vx

A:

Q: Find the arc length of y = 3x + 5 on 0 < x < 4

A: Consider the given curve, y=3 x2+5 ,     0≤x≤4

Q: What is the arc length of the curve of x5 y = + 10 1 6x3 from x=2 to x = 5?

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Q: -arc sin y dy 5 Answer with text and/or attachments:

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Q: The length of one arch of the curve y = sin x is given by L = | VI + cos² x dx. 0, Estimate L by…

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Q: Find the arc length for y = In(sinx) on [4' 4

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Q: Find the arclength on y = 4x3/2 from x is greater than or equal to 1 and less than or equal to 3

A: given: the function is y=4x32. we have to find the arc length on y=4x32 from x is greater than or…

Q: er dy %3D sec da

A: The given differential equation is exdydx=sec y and the initial condition is y0=1. Solve the given…

Q: Integrate this item using (parabolic) Simpson's rule, with interval width of 2.00 units. x tan x +…

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Q: 9. 2y(у? — х)dy — dx, when x %3D2,у %3D 2

A: Given that: 9.     2y(y2-x)dy=dx,    when x=2, y=2     NOTE: As per our answering guidelines, we can…

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.