Use the Fundamental Theorem Of Calculus and the Newton-Leibnitz rule to answer the following: 1. Determine d dx Z ln(x) e x tan(p t)dt:

Q: 1- Compare the results of the closed and open Newton-Cotes formulas when approximating a) x In x…

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Q: If tg(t)dt = sin(x) for every x, find g(2 1). g(2 x) =

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Q: 19.Show that W[eλt cos(μt), eλt sin(μt)] = μe2λt.

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Q: 1) By using the fundemantal theorem of calculus to find f(x) where d. Vi+3 dr and use f(t) =/? +3 dx…

A: The fundamental theorem of calculus is:  ddx∫axf(t)dt=f(x)ddx∫x4x6t5+3dt=ddx∫ax6t5+3dt-ddx∫ax4t5+3dt…

Q: Show that g(t) = t² tan t takes on the value for some t in [0, 4J.

A: Given Data The equation is g(t)=t² tan t. The interval is [0, π/4].   Put the value for t=0 in…

Q: If g(x) = ªſ*'[e'− In(2t+1)]dt, find g ''(x) . - dx -2 4 A + (2x + 1)2 Be-In(2x+1) 2 C (2x + 1)² 4 D…

A: Given that,      gx=ddx∫-2xet-ln2t+1dt

Q: Differentiate d/dx  ∫ [cos(x), 0] t dt (using the Fundamental Theorem)

A: Differentiate d/dx  ∫ [cos(x), 0] t dt (using the Fundamental Theorem)

Q: Solve the D. E. to the I. V. P. sinx(e- + 1)x' – cosx = 1, y(-) = 0 (1 + e") (1 – cos x) = 2 O (1 +…

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Q: Solve the D. E. to the I. V. P. sinx(e + 1)x'- cosx 1, y() = 0 O (1 + e') (1 + cos x) = 2 O (1 + e)…

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Q: Solve the D. E. to the I. V. P. sinx(e + 1)x' – cosx = 1, y(0) = 0 COSX O In (1 + cos x) = 1 + e (1…

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Q: If r (t) = (sin(t), cos(t), 2), then ſr (t) dt = 0.

A: The vector function is given by rt = sin(t),cos(t),2 To evaluate : ∫0πrtdt

Q: Q1. Use the Fundamental Theorem Of Calculus and the Newton-Leibnitz rule to answer the following: 1.…

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Q: Suppose F(x)=∫7 to x (sin(t)/4+t) dt. Use the Fundamental of Theorem of Calculus to calculate F′(x).

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Q: Q1. Use the Fundamental Theorem Of Calculus and the Newton-Leibnitz rule to answer the following: 1.…

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Q: A. Solve the following 1" order, non-homogeneous linear ODE: dy cos? x sin x +y (cos x) = 1 dx

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Q: Given Lve f(t) dt = In(x) cos(x) + sin(3) :L.e- f(t) dt, find f(x). sin(3)

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Q: Solve the D. E. to the I. V. P. sinx(e-y + 1)x' – cosx = 1, y(0) = 0 %3D %3D (1 – e') (1 + cos.x) =…

A: We will find out the required solution.

Q: The integral cos(x – 3) dx is transformed into , g(t)dt by applying an appropriate change of…

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Q: For f (x) = sin x + 2, there exists a 'c' in [0, 27], Which satisfies the conditions of Rolle's…

A: From the given problem:   fx=sinx+2 ;0,2π   For verify the Rolle's theorem:   1) f(x) is continuous…

Q: Q1. Use the Fundamental Theorem Of Calculus and the Newton-Leibnitz rule to answer the following: 1.…

A: Note: "Since you have asked multiple questions, we will solve the first question for you. If you…

Q: Q1. Use the Fundamental Theorem Of Calculus and the Newton-Leibnitz rule to answer the following: 1.…

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Q: Find the most general antiderivative of the following functions. (d).r(θ) = (sec θ − tan θ)^2

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Q: Which of the following is equivalent to: na ("e-"e cosh t dt 2 L [cos h t] L [e* cos h tl L [e #cos…

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Q: Find g(e) so that when u = g(x) the integral S: 1+lnx sec(g(x)) dx can be rewritten as ſ cos u du .…

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Q: Differentiate with respect to t. y = a cos t + 2 sin t

A: The given equation is y=acost+t2sint.

Q: If g(x) = | cos' t dt , then determine g'(x). %3D

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Q: . Solve the following problems: (a) Utt = 0, 0 0, u (x, 0) = x + sin x, Ut (x, 0) = 0, 0 0.

A: Solution

Q: Use the Fundamental Theorem of Calculus to calculate the following derivatives: 4 d (a) d.r cos(4t²)…

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Q: Differentiate the following functions: e2x+1x +2 .3 a) f (x) = sin (3x+2) %3D -1 sin(3x) V3t? +t-3…

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Q: Solve the questions given below using the Fundamental Theorem of Calculus. cos a 1 dt, where g(x) =…

A: Introduction: When we perform differentiation of a function that is represented under the integral…

Q: S sin x In(cos x) dx

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Q: Q1. Use the Fundamental Theorem Of Calculus and the Newton-Leibnitz rule to answer the following: 1.…

A: Given: I=ddx∫exlnxtantdt For finding value of given expression, we use fundamental theorem of…

Q: Given f(x.y) = e X cos y, Evaluate fx(2,0) e2 cos 2 O sin 2

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Q: f(t) = et+1 cos t. f(t) = eat43/2_ f(t) = eat cos 3t.

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Q: Use Part 1 of the Fundamental Theorem to simplify the following expressions.

A: To find the derivative of the integral, one need to use fundamental theorem of calculus, by…

Q: Solve the questions given below using the Fundamental Theorem of Calculus. r9(x) If f(x) = 1 rcos a…

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

Q: 1 Compute L a) f(t) = e t 母地- ecos t Cos t c) f(t) = e 'sin t d) f(t) = et cost e) none

A: The given function is, L-1s+1s2+2s+2

Q: Solve the following problem dw dw + x dt 1, -00 0, %3D dx with w(x, 0) = f(x).

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Q: Given that f (x, y) = y ln x cos x, find fæærzay (T, 1). Keep your answer to three significant…

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Q: Use Fundamental Theorem of Calculus to evaluate the following: d a) sin t dt dx

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Q: Suppose r E C[0, 1]. Show that there exists unique y E C[0, 1] such that x(t) = y(t) + 2 5 sin(s +…

A: Consider the provided question,

Q: It is definend as (Tf) (t) = S sin?(x – t)f(t)dx ,with fe [0,1] 1) is T: c [0,1] → c [0,1] defined…

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Q: Does the fundamental theorem of calculus imply that e' dt = e*?

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Q: Prove that d/dx [cos x] = −sin x.

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Q: Which of the following is the result when the Fundamental Theorem of Calculus is used to evaluate…

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Q: Give a physical interpretation of JT. F.ndS.

A: This expression is of surface integral for calculating the area of the field bounded in the…

Q: If r = sin (ƒ(t)), ƒ(0) = pai/3, and ƒ′(0) = 4, then what is dr/dt at t = 0

A: Given:

Q: 1 Use the substitutions given to find fI+x dx; u = 1 + x + sin x dx; u = sin x cos x a

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Q: Using Part I of the Fundamental Theorem of Calculus, 8 d evaluate: dx t7 dt =

A: Given that ddx∫x8t7dt

Q: Solve the following DE: [2х+ усos(ху)] dx + x cos(xy) dy%3Dо O sin(xy) - х2у? -с O cos(xy) – x?y? =c…

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