0.893 dx Va a>0, evaluate (x°e dx Knowing that Part 2. xe Using the result of problem 1 above, find 6(e +1)

Q: Question 4 -e-*) dx Evaluate: A '+C 2 B cosh x +C sinh x +C D – sinh x +C E None (F -cosh x +C 2

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Q: 1 s |49 – s2| ds = -14 49т? sin( x dx 14 dt = t2 – 14t + 50 ||

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Q: 31. f(t) = arctan(sinh t)

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Q: Find the solution of the equation = e cos y dy? which tends to zero as x → 00 and has the value cos…

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Q: QUESTION 3 (a) Use the trapezoidal rule with 4 ordinates to estimate the value of x + In (2x) dx,…

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Q: Evaluate e Cos I dx with tolerance e = 0.05 using the Composite Trapezium Rule. %3D

A: Equation is f(x)=ecos(x).The value of the table for x and y x 0 0.25 0.5 0.75 1 1.25 1.5 y 2.72…

Q: /x[cosh?( 2x²) – sinh²(2x²) ]dx is equal to (A) x?dx B) None © Sar dx (D 4 xdx E xdx

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Q: The change in heat radiated by a body, detected by a pyrometer (non-contact temperature sensor), is…

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Q: S 5 sin(3x)e2cos(3r)dx

A: Solve integral by substitution method:-

Q: 3) I= dx 4) I= f cos?x dx

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Q: x[cosh?(2x²) – sinh²(2r²) ]dx is equal to A xdx B xdx x²dx D None E dx

A: To find the given integral is equivalent to which integral.

Q: Solve the following initial value problem: dy y(0) = 8 %3D dx Then, find y(100) to the nearest…

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Q: Answer the following neatly and completely. Find dy/dx. 1.y = sin(x²e3*) 2.y = In (tan x?) .xcos y –…

A: Chain Rule of Differentiation : If we have y=f(u) and u=g(x) then dydx = dydu·dudx

Q: e) tan 5y – y sin r+3ry? = 9.

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Q: Given x2 + 11x + 30 dx 1 + cos?(x) At what value of t does the local max of f(t) occur? f(t) :

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Q: 5 dx, correct +2x²) Problem 19. Evaluate (3 to 4 decimal places

A: ∫0152x2+3dxSubstitute u=2x3→dudx=23→dx=32du=∫532(3u2+3)duSimplify:=523∫1u2+1duWe know that…

Q: a) Given that y= sinh'(cos(x)), provide detailed derivation to obtain the expression of dx

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Q: 5. Find (x +3)² dx, (be careful!) 5. e® + e¯ | cosh r de dx %3D

A: The complex form of integral can be converted to simple integral using integration by substitution…

Q: S(L* -1) (4 x²)dx Se* . sin e* dx Stan(3x +5) dx

A: 1. To evaluate: ∫x2-1·4-x2dx Solution: Power rule of integration states that: ∫xndx=xn+1n+1…

Q: Question 10 of 10, Step 1 of 1 dy Find dx Answer for the equation below. dx 11 8/12 Correct 4x4 +…

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Q: Find dy/dx for the given value of x y = tan-(In x) ; x= 1/e A. e В. е C. e D. Е. None of the above

A: To evaluate the derivative of the given function, apply the following formulas.

Q: 4. Solve for ſ e* sin x dx in the equation S e* sin x dx = e* sin x + e* cos x - Se* sin x dx + c.

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Q: find the most general antiderivative or indefiniteintegral. You may need to try a solution and then…

A: The given integral is ∫1x-5x2+1 dx. Evaluate as follows. ∫1x-5x2+1 dx=∫dxx-5∫dxx2+1=lnx-5tan-1x+C…

Q: 4. Find d2y/dx? for the following functions: a) y = sin x2 cos 2x b) y = cos (sec? 3x)

A: Given that  a)y=sinx2cos2x b)y=cos4sec23x find d2ydx2

Q: QUESTION 1 Find ay/dx?- X = t + sint, y = t- cost

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Q: ) S² e2x sin x dx T/2

A: To find the integration from 0 to π/2 e2xsinxdx

Q: (e) /s sin (x) cos (x) dx

A:

Q: 3) S cos(Inx) dx

A: according to guidelines we should able to do only one question at a time #3

Q: Given that 1 -dx + dr = ln a, find the exact value of a. V16+9x² V9+4x* 1.

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Q: 1.) Suppose p > 0. What is the relationship between n=1/i da and n+1 dx? Make sure to justify your…

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Q: Integrate the following functions: 1. S sin 2x dx

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Q: Q1: Find dy/dx for the following functions:- (1) e – 3* = x sinh y (2) tan-12 = (Inx' + y²)

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Q: 1) S“(cosx)" dx. 2) Г(-4). 3) В (10,9) 4) Sº x° e-2* dx Ja-x)i 5) o

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Q: 1. sin° 0 d0 =

A: First do some simplification than use substitution method to solve this.

Q: S S som'e dx cos'x

A: Perform integration

Q: We know that y dy? arctan (e*+1) so whats the value for dx 1 a) e2a+2 +1 1 Ob) els+1)* +1 Need This…

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Q: cos(z)ln (1 + æ²) + x3.7 dx. 3 Evaluate 3 1 + e1.87x – 66.1 answer = Question Help: D Video

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Q: A. Assimilation (Time Frame: Since we already presented S sin x dx and ſcos x dx, we can now do the…

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Q: Q) Find the general solution. dy sin-1x Iny dx II

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Q: Find dx implicitly, if e*(e♥ – 1) + sin(2x+ 5y) = In(v7) – dy 5 ·cot(2x - y+2

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Q: Q1/ Find of the following problem : dx e. sin- x) = y g. y = (x² – 2x + 2)e*

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Q: dy 4)y = sin-1) veriliyor. i bulunuz ve sadeleştiriniz. dx

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Q: (ei-e) dx +x cosh udu = 0 when x = 0; u = 0 1. %3D

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Q: 2. Given xy? =Sinlyz find dź/dk

A: We are given: x2+y2+z2=sinyz Differentiating both sides with respect to x, we have…

Q: x°lnx dx 3.

A: Given Integral,I = ∫x3 In x dx

Q: Find dy/dx of the following: a. y=sinh-5x b. y=sinh-e* c. y = cosh¹ √√x

A: To find dydx for the given y.

Q: Given that 1 -dr+ 1 - dx = ln a, find the exact value of a. V16+9x? V9+4x?

A: given: ∫01116+9x2dx+∫0219+4x2dx=lna we have to find the exact value of a.

Q: 1. ſ e*sinx dx

A:

Q: O Find the approximations T10, M10, and S10 for 10 sin(x) dx. (Round your answers to six decimal…

A: NOTE: According to guideline answer of first question can be given, for other please ask in a…

Q: Solve the following using the method of solving Bernoulli Equations. dy 1. dx +? = x²y?

A: Given:         dydx+yx=x2y2 This is of the form dydx+P(x)y=Q(x)yn…

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.