Sot.e-3t. sin 2t . dt f(t)

Q: e (a cos bx + b sin bx) a + b? ax Secos bx dx=-

A:

Q: c) dx E (sin cos) dt

A: We find ddx ∫xπ/2   sint2   cost3 dt

Q: 3. f(t) = 2e3t sin 2t – 3e3t cos 2t -

A:

Q: cos (z) = e+1 eiz+e-iz 2i eiz+e¯iz e+e 2i

A:

Q: T/2 cos(9t) cos(18t) dt

A:

Q: 2. /1+ cos² x dx dy = ? Isin¬' y -2/2 1 (a) 3 3 2/2 (b) 3 3 -2/2 (c) 1 3 3 2/2 (d) 1 3 3 V2 1 (e) +…

A: Given is multiple definite integral.

Q: 3) eYsinx dx = cos?x dy 4) y' + (÷) y = xy?

A: First question we can easily solve using veriable separable method. Second question we can use from…

Q: HW3 Find dCSe tsinht sint dt)

A: Laplace transferom of Integrals

Q: H.wl: Find L{e-3t St. sin 2t.dt p1 p2

A:

Q: If dy = x² dx, find the equation of the curve that passes through the point (1, 1). 2y + x³ + 2 = 0…

A:

Q: j) S (2 cos a – e) dx

A:

Q: (a) J x cos x dx

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: L(S,(3r² – cos t)' dt)

A:

Q: (b) dx cos(t) a

A:

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: OPnd w if ww=fcカっ) find メ= Sint dt

A: We have to find d2wdt2, Where w=f(x,y) and x=sint , y=t2 We will get  d2wdt2 by differentiating w…

Q: [ sec2t dt + S sin?t dt + § n'-1dt

A:

Q: 1. cos? 2t dt

A: Given query is to eveluate the integral.

Q: 24.(cos t) y″ + (sin t) y′ − ty = 0

A:

Q: e-t sin(v3t) dt (a) L

A: We have to solve given problem:

Q: •T/2 cos“ x dx. OS

A:

Q: d 27. dx ], cos t dt

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

Q: Sect sec't dt Tari'la)

A:

Q: f (t) = e3t sin(3t) – ťe*.

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: ? cos i dt

A: You must have idea about integration by parts.

Q: dw (C): If w = tan x and x = 4t³ + t ; Find ? dt

A: Let's do derivative of given function.

Q: dy dy and dr 1. Find if dr? x(t) = t2 – 2t y(t) = sin(t)

A:

Q: /4 sec? Vwdw a) b) sin 2.xcos xdx c) f tanh xdx

A:

Q: 3. [(3t S(3t +r²)sir sin(2t) dt

A: Please post multiple questions separately.We know…

Q: f(t) = cos(2t + 3) + e¬tu(t – 4) + tcosh²2t

A:

Q: Find dy/dx at the given point. (2t + 9, 7t − 9), t = 1

A: We have to find dy/dx at the given point - (2t + 9, 7t − 9), t = 1

Q: 1 and y' CO)

A:

Q: d²y +9 = cos?t+ sin? t + cosh t + sinh t +3 sint -3t dt %3D dt2

A:

Q: TE/7 b. π/3 Sa sin(t) dt

A:

Q: 00 | f(x) cos axdx = S2 – a,0 2

A: Value of f(x)

Q: A ) Find ſ cos 5t dt B) If y = x² + , x = 2t -5 then find dt

A: A)-     I=∫Cos5t dtlet 5t=uderivating both sides5 dt = duSo,I=15∫Cos u du = 15 Sin u +C…

Q: e) s = cos (1– 21) -2 4t f) y = t+1, .2 x + x g) y =

A:

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

A: given ft=e3t+cos6t-e3tcos6t

Q: Evaluate the integrals

A: To find the integral ∫0π4sect i+tan2t j-tsint kdt

Q: 18. dx/dt = e'(1 + sin t)/(1 + cos t). Answer: [x – e' (tan(t/2)) = C]

A:

Q: (a) e 20 sin(30) de (b) t sin(2t) dt 0.

A:

Q: i+ cż + x = cos t, e>0.

A:

Q: f zea I cos(2r) dr. (c)

A:

Q: cos(5r)ő(1 – 3) dt = e sin(t)6(t – 2) dt =

A:

Q: FCH)- O -t e Sin 2t dt

A: To find the below integral. ft=∫0te−tsin2tdt

Q: dt cos?(t) dr dx du du + ex- at cos²(t) :-7u, ex dr du -7u dr t(0) = 0, x(0) = a, u(0) = e et heR.

A:

Q: (e) y' +2y : = cos(2x)

A:

Q: (s-s?-t)ds + (t + s? +t?)dt = 0

A:

Q: 7π| A d) S_T/A (sin x + cos x) dx

A: We will evaluate the given integral in the following step.