Use the second Fundamental Theorem of Calculus to evaluate the following:

Q: Use the Second Fundamental Theorem of Calculus to find F′(x).

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Q: Use the Fundamental Theorem of Calculus to evaluate, Vx3 (x + 5)dx. 0.

A: To evaluate:                       ∫05x3 (x+5)dx

Q: 2. Use the First Fundamental Theorem of Calculus to differentiate the function f(r) = VI+ tª dt.

A: We will use the first fundamental theorem of calculus to evaluate the derivative.   The detailed…

Q: Integrate to find F as a function of x, and demonstrate the Second Fundamental Theorem of Calculus…

A: We need to Integrate fo find F as a function of x.

Q: 6. Use an appropriate substitution to prove f(r)dr = f(a + b – x)dr. %3D

A: We have to prove definite integral property.

Q: Evaluate the following integrals using theFundamental Theorem of Calculus.

A: We distribute the denominator.

Q: 2. Explain how to use the evaluation part of the Fundamental Theorem of Calculus to compute J", (3x²…

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Q: Use the Second Fundamental Theorem of Calculus to find F'(x)

A: The mathematical nature of the second fundamental rule of calculus is shown on the white board.

Q: Consider the following. F(x) = (a) Integrate to find F as a function of x. F(x) = (b) Demonstrate…

A: Given function:                               F(x)=∫8xt3 dt   To Integrate the above given function:…

Q: Let x, y be real numbers such that xy=1x and x≠y. Prove that x^2+y^2≥2\sqrt{2}|x−y|.

A: Given: xy=1x,x≠y To find: x2+y2≥22x-y

Q: Use the Second Fundamental Theorem of Calculus to find F"(x). F(x)= •Live+sa F(x)= x

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Q: 5. Use the Second Fundamental Theorem of Calculus to find F'(x). х 1 F(x) = S* dt.

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Q: Use the Second Fundamental Theorem of Calculus to find F '(x).

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Q: 8x2 F(x) Vt2 – 1dt

A: Given,         Fx=∫08x2t2-1dtWe know that,             The first fundamental theorem of Calculus…

Q: 2 178. 1x

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Q: Use Part I of the Fundamental Theorem of Calculus to find each of the following when f(x) = | t

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Q: Use the Second Fundamental Theorem of Calculus to find F'(x). F(x) 1+tdt F'(x) =

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Q: (b) | sin(x) – 7dx -

A: ∫0πsin(x)-7 dxLet the lower limit of integral is a and the upper limit be bSo now according to the…

Q: (x²-3x+1) dx

A: Given that ∫23x2-3x+1dxSolution :∫23x2-3x+1dxx33-3x22+x23333-3322+3-233-3222+2

Q: Use the second fundamental theorem of calculus to find F'(x)

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Q: Use the Fundamental Theorem of Calculus to cvaluate (1 - da

A: Integrate using fundamental theorem of calculus.

Q: „T/2 sinOdo 183.

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Q: Integrate to find F as a function of x, and demonstrate the Second Fundamental Theorem of Calculus…

A: Integral is F(x)=∫4xt32dt

Q: Use Part I of the Fundamental Theorem of Calculus to find each of the following when f(x) = | t*dt…

A: By using Part I of the Fundamental Theorem of Calculus:f'(x)=x4

Q: Use the Second Fundamental Theorem of Calculus to find F '(x). F(x) = + 9 dt F '(x) =

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Q: Use the Second Fundamental Theorem of Calculus to find F′(x).

A: To find F'x using the second fundamental theorem of calculus: Fx=∫-1xt4+1dt Solution: The second…

Q: Use Part I of the Fundamental Theorem of Calculus to find g'(x) : g(x) = /47² – 3t dt coshx V4t² –…

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Q: Use Euler’s Theorem to find the degree of homogeneity for f( x1 , x2) = x3 + y3 + 3xy2

A: We will use the Euler's theorem which is : x•fx + y•fy = nf  Where, n = degree of homogeneity    The…

Q: G'(0), where G(r) =| e * dt

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Q: Let f(æ) = In(z') f'(2) =

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Q: Evaluate each definite integral using the Fundamental Theorem of Calculus, Part 2. 181.  16 ∫…

A: By Fundamental theorem of calculus .part 2  ∫abf(x)dx=F(b)-F(a) where f(x) is continuous on the…

Q: Prove Equationally that F A → B → A.

A: Given: ⊢A→B→A

Q: (3x² + 5x-2) dx

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Q: Given that F(x) = a) F'(x) bl 5'(4) 2 1 1 + 2 dt.Using the 2nd Fundamental Theorem of Calculus, find

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Q: Use the first fundamental theorem of calculus to find F'(x) F(x) = [ cosr' dt

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Q: Use the second fundamental theorem of calculus to evaluate the following: x, x 20 10. [* f(x) dx if…

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Q: t dt. Use Part I of the Fundamental Theorem of Calculus to find each of the following when f(x) =|…

A: f(x)=∫3xt7dtf'(x)=ddx∫3xt7dtBy fundamental theorem of integral calculusf'(x)=x7

Q: 2x* dx

A: Here is the solution

Q: Integrate to find F as a function of x, and demonstrate the Second Fundamental Theorem of Calculus…

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Q: Use Part 1 of the Fundamental Theorem of Calculus to find each of the following when f(x) = t³d =…

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Q: Use the Second Fundamental Theorem of Calculus to find F '(x). F(x) dt F '(x) =

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Q: Use the first fundamental theorem of calculus to find F'(x) F(x) = cosr' dt

A: In this question we have to find F'(x).

Q: Let f(x) = ∥x∥. Find out its conjugate function f ⋆ and prove your conclusion.

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Q: Use part I of the Fundamental Theorem of Calculus to find the derivativ f(x) Vt3 + 2°dt f'(x) =…

A: Given query is to find the derivative.

Q: The Fundamental Theorem of Calculus says that f(x)da = F(a) – F(b) provided f = F' Is continuous on…

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Q: d cx2. -x csctdt d dx J4

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Q: II. Use the first fundamental theorem of calculus to find F'(x) .Write your final answer on the box.…

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Q: Use the Second Fundamental Theorem of Calculus to find F '(x). F(x) = VE4+1 dt F '(x) =

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Q: In Exercises 5-34, use the Fundamental Theorem of Calculus Part 2 to evaluate the definite integral.

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