Consider the following. x = t - 2 sin(t), y = 1 – 2 cos(t), 0sts 9n set up an integral that represents the length of the curve. 9m dt Ise your calculator to find the length correct to four decimal places.

Q: Find the value of integral | (x + y + z)ds, where C is parmeterized by 7(t) (12 sin(3t), 10 cos(3t),…

A: Let’s suppose that the three-dimensional curve C is given by the parameterization, x=x(t), y=y(t),…

Q: Find the value of integral | (x + y + z)ds, where C is parmeterized by F(t) = (12 sin(3t), 10…

A: Given: ∫C(x+y+z)ds, where C is parametrized by r→(t)=12sin(3t), 10cos(3t), 211cos(3t) for 0≤t≤π.

Q: Consider the following integrals 4 sin? x -dx x2 + 6 00 e9t dt i. e9t – 1" Mark the correct one for…

A: Step:-1 Since, we know cos2x = 1- 2 sin2x⇒2 sin2x = 1 - cos2x An integral is called convergent if…

Q: 5πT sin' cos dx 4х 8.

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Q: dz evaluated at dt If z=tan In with x=sec t and y=eª. Then the value of t= 0 is equal to ...…

A: Chain Rule Let us consider the function z=f(x,y) where, x=g(t) and y=h(t) Differentiate the function…

Q: 4 dx 1/2 v1-x²

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Q: (b) Use residues to evaluate the following definite integral: de 6+5 sin 0

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Q: (a) Find the differential dy. y = rad(15+x2) (b) Evaluate dy for the given values of x and dx. x =…

A: a)   The given function is y=15+x2. The differential of y is,…

Q: y=sin

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Q: After integration by parts we have e70 cos(80) d0 e70 sin(80) d0.

A: Explained below

Q: Q₁: Evaluat the integral:- 플 S S. sec (cosx) dx dy Sin y

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Q: Evaluate the following integrals. (a) ∫ x3 ex2 dx (b) Find the values of a and b for the curve…

A: (a) Consider the integral: I=∫x3ex2dx……1

Q: Given the integral J 12cos(5x) dx Use the integral table to help you find the Anti Derivative of the…

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Q: In the following equation/s, find the indefinite integral :-   see the equation attached here

A: We have to calculate the given integral   the given integral is

Q: The velocity of a particle moving back and forth on a line is v = ds/dt = 6 sin(2t) m/sec for all t.…

A: Given:

Q: The displacement of a structure is defined by the following equation for a damped oscillation: y=9e…

A: The displacement of a structure is defined by the equation  y=9e-0.7tcos4t…

Q: Find the differential of the function. y = V 4 + cos(0) dy =

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Q: 2л I7 ở sin(4)dp do dp 0.

A: To evaluate: ∫0π∫02π∫05p2sinϕdp dθ dϕ Evaluating the given integral, ∫0π∫02π∫05p2sinϕdp dθ…

Q: Find the value of following the integral: ☎ COS²T -π1+a* S². dx,a>0

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Q: 1. Differentiate the following: G(t) = sinh(In t) %3D G (t) = ? a. Cosh 3t b. y = ?

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Q: a) Find the differential du. x/4 dy=? b) Evaluate dy for the given Nalue of x and dx X= 0, dx = 0.I…

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Q: 1. Evaluate the following integrals: '1 36" dx 6* + 3 (a) cosh x + ecotha sinh? x sinh x - (b) dx 4…

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Q: b) sec* 0 d0 Give the exact answer.

A: The given integral is ∫π4π3sec4θ dθ

Q: Approximate the following integrals using the Trapezoidal rule. -0.35 2 -dx x2-4 1. 2. Só x sin(x)…

A: 1.The given integral is, ∫00.352x2-4dx Here, f(x)=2x2-4,taking h=0.05 Let us construct the table as,

Q: Find dw/ dt at the given value for the following functio 1) w=x² + y°, x = cos(1), y = sin(t), at †…

A: The given functions are w=x2+y2, x= cost  and  y=sint and t=π. Evaluate w in terms of t as follows.…

Q: Find the differential dy of the given functions . (Use "dx" for dx.) a) y = 2x − (sin(x))2 b)…

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Q: (a) Find the differential dy. y = tan(x) dy = sec?(x) (b) Evaluate dy for the given values of x and…

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Q: Let Y(s) = L [8et sinh(11t) + sin? (11t)] Evaluate Y(s) at s = 1. Round your answer to three decimal…

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Q: Find dw/ dt at the given value for the following functions 1) w=x² + y²₁ x = cos(t), y = sin(t), at…

A: Sol

Q: integrate ƒ over the given region. ƒ(s, t) = es ln t over the region in the first quadrant of the…

A: The given function is fs,t=eslnt over the region in the first quadrantof the st-plane that lies…

Q: Find the differential and evaluate for the given a and dæ. sin(5z) 1 * = -T. dx 0.75 %3D dy Preview

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Q: Given 4 cos(x²) dx 2 How many Trapezoids will you need to estimate the definite integral to an…

A: Given the integral I=∫24cosx2dx. (a) We need an accuracy of 0.001 when the Trapezoidal rule. The…

Q: Question 13 Evaluate the integral J sinh? (2x)cosh(2x) dc sinh“(2x) +C A sinh(2x) +C B 9 costf(2x)…

A: Use the derivative identity, ddx(sinh(ax))=acosh(ax) And the power rule of integration is:…

Q: Hiw@ Find dy for the dollowinge りょ CasX +x+ 2) 1 = TE よ + Sec( x) TT InX + T +linx)

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Q: Find the differential of the function. Z = e cos(2nt) dz = dx + dt

A: Given,

Q: 13. 2xy dx + y“dy= 0; y(0) = 1. Answer: [2r² + y² = 1]

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Q: 11. Put the following equation in separated form, do not integrate. dy C. dx = sec (y)e*->(1+ x) d.…

A: we have to make in separable form

Q: Evaluate the line integral ( 9х + 5у)da + (х — у)dy along the curve C : x = 6 cos t, y = 12 sin t…

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Q: Find the value of integral | (22 + y² + 2)ds, where C is parmeterized by F(t) = (cos(4t), sin(4t),…

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Q: ad the indicated integral (if it exists) E dz +1

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Q: Find the following integral. Note that you can check your answer by differentiation. / (t+ 1)? t2 dt…

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Q: Find the f(x)=6" locol mayt local miu for te t St -14 dt COS 'x)= x + Sx -14 cosz t) tI 2. %3D

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Q: Find and simplify the following integrals: S dx 11) (x-2)² 12) ſ cos(2x)e sin (2x) dx

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: The velocity of a particle moving back and forth on a line is y = ds/dt = 6 sin 2t m/sec for all t.…

A: given the velocity of a particle moving back and forth on a line is y = ds/dt = 6 sin 2t m/sec for…

Q: (dr Ifr=a cos ti +a sin tį+ at tan 0 k, find dt dr at t = 0. dr?

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Q: 10 cos(x) Evaluate the improper integral: / dx Vsin(x) а) 30 b) O20 40 c) 3 d) Odiverges e) 10

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Q: (3) Evaluate the following indefinite and definite integrals: (a) ſ(x³ +e* )dx (b) 1 |dx + XVx -1 2…

A: We will evaluate the given integrals as shown below

Q: An object moves in one dimension with avelocity in m/s given by v(t) = 8 sin ∏t + 2t. Find its…

A: Given: The velocity of an object in m/s is given by  v(t)=8sinπt+2t Time interval is t=0 to t=10

Q: Find the differential dy and (b) evaluate dy for the given values of x and dx. y=ex/10 , x = 0, dx…

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