S(x) = 2 cos(4x)

Q: 4. e2x sin e*d x, use algebraic substitution

A: Given :  Intergral ( e2x sinex dx)

Q: 2. cos?x dx =x+ sin 2x + C X_SO

A:

Q: -y = tanh" (cos e* ) ||

A:

Q: fe²x+Inx² sin x² dx = +√e²x cos x² dx

A:

Q: If y = cos? x – sin? x, what is y? X - х, | dx

A:

Q: sin () (cos (t*) + t)dt %3D (2), NOTE: Enter a function as your answer. Make sure that your syntax…

A: In the given question, the Fundamental Theorem of Calculus Part I is applied. ∫afxgtdt=gfx·f'x

Q: If the following eq. is exact, then solve it (y cos x + 2xe) + (sin x + x²e + 2)y' 0.

A:

Q: re SE cos (x- In(x))dxdy

A: Since,  the  given  ∫y=1e∫x=1e1y  cos x-ln x  dx dywe  have  to  find  the  value  of the given

Q: Recall that cos™ 1 x = arccos x. Find r1/2 a sin(cos a) d. 1

A:

Q: If sin x - x sin x = -y cosx , then (y - 1) sin x = ? da C- x sip C+x sitft (B C - x COSX C+x COs

A:

Q: 9) 4+Snik dx = [ca CosX coJX dx

A: 9. Here given

Q: 5 sin?(t) cos“(t) dt

A: ∫0π5 sin2t cos4t  dt=5∫0πsin2t. cos2t .cos2t dt=5∫0π sin2t ×1sin2t cos2t dt=5∫0πcos2t…

Q: (c) Show that e* sin(x²)dx < e – 1.

A:

Q: dy cos?x sin x + (cos'x)y = 1 dx

A:

Q: e (1+x) sin (xe" )dx Evaluate sin (xe) +sin

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Q: 2х —1 The value of| dx is 1+x-x, tan А. 1 В. О С. 1 D. 4

A:

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

A:

Q: Evaluate ∫ a cos x dx and ∫ a sin x dx, where a is a constant.

A: Given∫a cos x dx

Q: 2n 3. o (x + cos x) dx

A: Given :

Q: If ſ x sin x cos x dx = xsin²x + Ax + B sin 2x + C, what is the value of A + B?

A: The given integral is, ∫xsinxcosxdx=12∫x(2sinxcosx)dx=12∫xsin2xdx=12∫xsin2xdx=12I1

Q: a) y = cos(e 2x) (e2x) -1

A: Differentiate wrt x

Q: Let f (t) = te" + e t sin 12tFind L{f (t)}

A:

Q: 2. Find cos ec (In x) dx . x1+ cot(h x)

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Q: Differentiate the expression y = e* cos x²

A:

Q: S 1+cos(3x)dx

A: Given : ∫1+cos3xdx

Q: 2) y = e°(sin e + cos e)

A: I understand that we need to find the derivative of this function as nothing is mentioned

Q: n(en sin-lx ) dx cos(sin -lx) +C Vī-x? 1–x2 A) True B False

A:

Q: 1. Compute 2x ecos cos sin 2.x dx e. Compute CT/4 sin* 2x cos 2x dx

A:

Q: e 9. cos(x) dx - " sin(x) dx. Evoluate

A: Formula:∫ cos x dx = sin x + C∫ sin x dx = - cos x + C

Q: +6 cos(x³) A True B) False |dx=0

A:

Q: ez² cos(z) dz .

A: In this question, we use the Cauchy theorem for f(z).

Q: Please find all 0 < 0 < 2m, for which (a) tan () = V3 b) 3 sin? (0) +4 = 5 (c) 2 cos(ln(x² + e") = 3…

A:

Q: S sin(ax)cos(ax)/3 – cos(2ax) dx

A: Sin(2ax) = 2*Sin(ax)*Cos(ax)

Q: Is the following equation exact or not?. If exact, obtain the General Solution to the following…

A: Is the following equation exact or not?. If exact, obtain the GeneralSolution to the following ODEs.…

Q: (ii) Evaluate J dx. COS TI

A:

Q: al Evalluate; I. cos X AX V sin x Hints sin'x+cosX-4

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Q: 3. |2" – 8| dx sinh? (e-) 4. dx e cosh(e-*)

A:

Q: 0 sin√xcos√x √x dx is equal to

A: To solve the given integral

Q: 3a. cos πx sin πχ dx

A: We need to integrate the given expression. ( As per our policy, we can solve 1 question at a time.…

Q: Simplify the lefthandside so that LHS = RHS: 2 1+ cos(t) 1 – cos(t) 1 1 sin(t) tan(t) %3D %3D 1+…

A:

Q: QUESTION 2 If y-sin-¹ z, show that d'y Hence, deduce that -(1)-(2) - <- 0. dz = M dz dz

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Q: y 2+ TT 3 2 -2+ -37

A:

Q: 3 Cos |X TT 13) y = 3

A: We need to plot the graph of given curve:

Q: If y= cot"+ tan-1x?), then dy dx x2 Select one: 2х + 1+x*' 1-x4 2x O a. 2x O b. 1+x' 1+x? 2x Oc. 2x…

A: All given options are wrong. See the attachment

Q: Part B. Find dy/dx in simplest form. Question 5 sec" x sec³x y= 7 5 Use the editor to format your…

A:

Q: sec x + coOS x dx 2 cos x

A: To evaluate

Q: sin x dx 1+ cos2 x 31. T/2

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

Q: (cos x cos y – cot x)dx – sin x sin y dy = 0

A: Given Equation  (cosxcosy - cotx)dx-sinxsinydy=0 Given equation is in the standard form Mdx+Ndy =0…

Q: From the definition (Equation 4.46), construct »¡ (x) and n2(x). 1 d je(x) = (-x)' 1 d ; ne(x) = -…

A: The definition is nl(x)=-(-x)l1xddxlcos xx.   Substitute  n=1 in nl(x)=-(-x)l1xddxlcos xx.…