sint dt (2. cos t3 Select one: 1 A (2. cos t? B. 4(2• cos tj +C OC2 (2. cos t +C D_ 2(2+ cos tj +C

Q: cosysin2xdx – (cos?y – cos?x)dy 0 when y(30°) = 30° %3D %3D -

A: Solution is given below:

Q: Find the length of the curve. cos(4t) i + sin(4t)j + 4 In(cos(t)) k, 0 <t< n/4

A: We have to find the length of curve.

Q: Evaluate the integrals

A: First of all use the trigonometric formula that is 1-sin2x=cos2x in the given integral to simplify…

Q: z = 2e"žsinx – 3e*cos(y) Ве find: www a²z a2z (n az а) дхду"") дудх ,b) ду

A:

Q: The integral (cos(3x))sin(3x)dr under the change of variable u = cos3r becomes ưdu. 9/29 Select one:…

A: Given integral:

Q: Transform F(s) (giving you cos 5t + t³

A:

Q: 4 sin' t cos tdt 4 sin"(t) cos (t) %3D

A:

Q: cos²x sinx dy + (y cos³x - 1)dx = 0

A:

Q: S₁ + Sa cos²0 de 01/2000 sin ²0 de csc ³0 de + Sc 01/se sec ³0 de The integral dx (x²+4)² can be…

A: We have to solve above integral

Q: 8. y = sin(cos7x) %3D

A: It is given that, y=sin(cos7x)   It is known that the derivative of sinx is cosx and derivative of…

Q: T/2 cos t dt 1 + sin²t

A:

Q: The integral (cos(3x)) sin(3x)dx under the change of variable u = cos3r becomes u du. Select one: a.…

A:

Q: Evaluate ſe* 2x cos 2x dx cos 2x a) 2esin 2x + C b) -+c 2 c) ecos2x +c sin 2x e d) – +c

A:

Q: dy of the following functi de A5) Find (a) y = sec(5r)[0.25 mark] (b)y = sin5x + cos6x [0.5 mark (c)…

A:

Q: cos(3t) sin(8t) dt

A: we use  2 cos A sin B = Sin(A+B)-sin(A-B) sin(-x)= sinx

Q: 4. Cos x=0.691 Ix = 46.291 %3D %3D ly = 43,709° A = B = H%=

A: Given cos x =0.691

Q: ∫cos(3t)sin(8t)dt

A:

Q: a. The velocity of a car in meters per seconds travelled from its origin is given by v(t) = In (t2 +…

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Q: Q3.a) Find if y + SE rsecx -dt = xy sint+1 dz Q4.a) if z = sin²0, and 0 = w² + cos (w) find-

A: 3a):  y+∫xsecx11+sintdt=xydifferentiate both sides and use Leibniz rule for differentiating the…

Q: derive 8t sin t (d) s %3D cos t t5

A:

Q: Find dy/dt. y cos (rtt-10) %3D Select one: A. -5T COs (Tt - 10) sin(7tt - 10) B.-5Tt sin (rtt - 10)…

A:

Q: Evaluate. S cos a In(secz)dr COS D

A:

Q: cos° (2t) 23. sin (2t) dt

A: Use the formula sin2x+cos2x =1.

Q: (c) h(r)- (r- 2r)(r+) (d) j(r)= COS T 1- sinr *cos2tan r (e) f(r) Page 2

A:

Q: 3. f(t) = 2e3t sin 2t 3est cos 2t %3D -

A:

Q: For a cosine function with amplitude A=0.75A=0.75 and period T=10T=10, what is y(4)y(4)?

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Q: Which of the following is equivalent to u=-cost+v3 sint ? a) u = 2 cos t +- 1 b) u = – cos| t+ 2 3…

A:

Q: Find the highest point on the cardioid r = 1+ cos 0.

A: We cal solve the problem by doing the derivative and set it to zero for finding theta.

Q: i. Jsin xcos 2x - sin 2x cos xdx

A:

Q: f(t) = 5e-3t – 3 cos 3t + 6 sin 5t – 9. %3D

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Q: cos e de =_ %3D • 2 • -T • 6

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

Q: dt 1. cos (2 sin 2r) V1-4r

A:

Q: Q1 Evaluate 1, where: -So I = -3x cos 2x dx

A:

Q: (a) f(t)=2+3sint- 2sin3t – cos5t (b) f(t)=1-sint +2cost- cos2t + cos3t - 2sin3t (c) f(t)= sin? t…

A: Given: (a) f(t) =2+3sin t -2 sin 3t -cos 5t (b) f(t) =1-sin t +2 cost -cos 2t +cos 3t -2 sin 3t (c)…

Q: Show that r = cos(2pi) is symmetric about the y-axis.

A: The solution of the problem is given in the next step.

Q: f(t) = e3t + cos 6t – e3t cos 6t ; L{f(t)} =? %3D -

A: given ft=e3t+cos6t-e3tcos6t

Q: A particle moves according to the position function s (t) = e2t sin (3t). %3D

A: Definition used -                        v(t)= dsdt                       a(t)=dvdt=d2sdt2…

Q: Use an appropriate local linear approximation to estimate the value of cos(59°). cos(59°) ~

A:

Q: f(8,t) = cos os(0e*) + cos( + e*) = COS + cos (s+

A: Find partial derivative.

Q: Q2) a) Find an® sec²y dy b) Is cos4xv2-stn4x dx = (2- sin4x) +Ctrue or false? show me

A: Use fundamental theorem of calculus for part (a)  For part (b) use substitution method

Q: ,In sec²(sin2y)dy can be evaluated by writing it as sec2y ! / sec²( sin2y) - 2 cos2ydy S. | sec2(…

A: To simplify the given integral.

Q: t/2 SL cosx/1+ cos²xdxdy is equal to 0, siny

A: Consider the iterated integral, ∫ab∫f1xf2xfx,ydydx In this iterated integral, the integration is…

Q: Hf sin x = A + B cos 2x +C cos 4x, then A = %3D C =

A:

Q: : s ech[In cosx]tanx dx Evaluate: A None - 2 tan-1(cosx) + C 2 tan -1(e cosx) + C CoSx (D - 2 tan…

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Q: cos (2t) 23. sin' (2t) dt 3

A:

Q: Cos Vt dt 3. Evaluate

A: The integration of the given integral is; Cos√t/√t.

Q: Find a trig substitution r = f(@) that makes 1 dr = cos 0 de. (V4+)3

A: Here we have to substitute x =f(θ)

Q: The integral . (cos(3x))'sin(3x)dr under the change of variable u = cos3r becomes v u'du. 9/29

A: