Q1. Use the Fundamental Theorem Of Calculus and the Newton-Leibnitz rule to answer the following: 1. Determine In(x) tan(VE)dt. dr

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Q: 1 4. First, make a substitution and then use integration by parts to evaluate [Hint: Use the fact…

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Q: a. Evaluate the following derivative d tổ tan(t) dt. sin(x) dx

A: We will use the Newton Leibniz formula to evaluate the differentiation

Q: Apply the Fundamental Theorem of Calculus to get the following derivative. d. In( t?+1) dt dx 1

A: Given, fx=ddx∫1x3lnt2+1dt To Find: f(x) by applying fundamental theorem of calculus.

Q: Evaluate the indefinite integral. 2 (t) – 7e' + 8 + 1 + 12 2 sin(t) – 8 cos(t) + sec- dt = +C.

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Q: Apply the Fundamental Theorem of Calculus to get the following derivative. d In (t² + 1) dt dx 1

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Q: tan x dt+ 1+ t? (1+ f')* 1 -dt=D1 1/e Ve prove LHSis equal t RHS

A: This question is related to integration. We solve this question we divide this question in two part…

Q: Prove that sinh−1 t = ln(t + √t2 + 1 ).

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Q: Differentiate g(t) = (at + 1)2 with respect to t. Assume that a is a positive constant. g'(t) =

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Q: 1 use the formula L = dt to find the length of the curve dt dt 1 X = y = t° for 0st s1

A: according to the guideline, we are allowed to answer the only the first question  please repost…

Q: P (a, b) = So -at² _e-bt2 dt %3D t2

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Q: Calculate the derivative e10x de L9 In (t)dt using Part 2 of the Fundamental Theorem of Calculus.…

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Q: Find G(1), G'(0), and G'(π/4), where G(x) =

A: Here we have;  G(x)=∫1xtant dt

Q: 2m 28. t sin 2t dt

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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: F(x) = sin t dt, [0,1] 0. F(x)]

A: The following formula for Maclaurin's series expansion of sin x will be used: sin x=x-x33!+x55!-...…

Q: Use Part 2 of the Fundamental Theorem of Calculus to find th. derivatives. dt sin y dy 1+ y? (b) dx…

A: Consider the integral ∫axfydy, where a is a constant. Note that, ∫axfydy will be a function in x.…

Q: d?y taby = Fo cos ot, where wo, ware positive con- dt- stants, and Fo is an arbitrary constant. You…

A: Given differential equation, d2ydt2+ω02y=F0cosωt      ...(1)

Q: 1. If F(x)= = cos a sin r (√t-1)' dt, find F'(x).

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Q: 1. Use the Fundamental Theorem of Calculus to evaluate the following (DO NO 5x -6x dx 1 | cos (x)--…

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Q: Use at least two methods to prove that dr/dt=0 when r=√x2 + y2, x=α cos t, and y=α sin t if α is a…

A: First method   r=x2+y2r=(α cost)2+α sint2            since x=α cost and y=α sint  =α2cos2t+α2sin2t…

Q: If f (x)= [a(«) =os* '(5) [1+ sin(t?)] dt find f 1 dt, where g(x) V1+t3 COS X

A: We need to find value of derivative.

Q: Evaluate the integrals

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

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: The equation implicitly defines z as a function of t. Find dz dt 11 dt cos (3 z) = -8

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Q: 15. Find the derivative of each of the following functions. TE-2 dt (a) f(x) = /" eV7t-2 %3| (b)…

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Q: 1) f(t) =t cos(@t) 2) f(t)=tsin(@t) 3) f(t) =t cosh(at)

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Q: d rx Cos t dt dx J-x Vt2+1

A: Definition used -                 The first fundamental theorem of calculus -…

Q: valuate |v(t)dt 1

A: We have given a graph in which the velocity v(t) of an object moving along a line is given where…

Q: 9. f (t) = In(t®) - cos(4t) +9 sin(2t) +e7t %3D

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Q: Express in the form x + jy (3) sin(t/4+j2)

A: Complex Number Question

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

A: In the given question we have to solve the question (1) and (2) (1) Determine ddx∫exln(x)tan(t)dt…

Q: Given z = sin(1 - 2). x = 2 – ts and y = 2t – s - then calculate when t = -1 and s = -1. dt

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Q: tanh (22) d) evalvare J seen 2 (2n ) e レッ using a substitution Suitable

A: To evaluate the given integral.

Q: 13. F(x) = sin t dt 20

A: We need to definite integral properties  also integral of sinx is -cosx

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

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Q: 2. u(x)= secx+à So u(1)dt.

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Q: 2.f (t) = cosh wt sin wt

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Q: ydx -( x+***ty? dy = 0

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Q: Use Part 2 of the Fundamental Theorem of Calculus to find the derivatives. d/dx ∫_0^x▒〖e^√t dt〗…

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Q: 10. Find the indefinite integral. Te cos 3t dt dv u = du = v =

A: Given integration is : ∫e9tcos3t dt   To find the value of integration.

Q: Consider the function g(x) = 5 S cos t dt – x?. Then g' (x) is

A: Given gx=12∫x4x2costdt  -x2

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

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Q: Show that g(x) = cos 2 =x+3 ™K(x, t) g(t) dt 0 || sin x cos t, 0≤x≤t Y sin texr

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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: (e) S x³ cos(x²)dt (hint: use substitution first) VT/2 COS

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Q: Consider the following. dt (4 + t? Let t = 2 tan(0) and determine the following. 2 sec-(0) dt = de t…

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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: Find the indicated derivative: d/dt ( (t^3 +3, 3t^2 -4)* (tan(t),sin(t)) )

A: We have to Find the derivative of d/dt ( (t^3 +3, 3t^2 -4)* (tan(t),sin(t)) )

Q: Q2: find dw/dt at given value point for the following function x= cos°(1), y = sin²(1).= =-. 1 at t…

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