State and prove the first fundamental the orem of calculus and its importance?

Q: Use the Fundamental Theorem of Calculus, Part I, to evaluate d de -dt

A: We have to find

Q: 2° dt

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Q: Use the fundamental theorem of calculus part 2 to evaluate the 16 integral: S 3/rd 9 Note: Convert…

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Q: Prove Taylor's theorem.

A: The objective is to prove Taylor's theorem. According to Taylor's theorem we have, If fx be a…

Q: 2) /4 sec'td

A: 2) Given that : The integral is ∫0π4  sec2 t dt .

Q: How is Green’s Theorem similar to the Fundamental Theorem of Calculus ?

A: How is Green’s Theorem similar to the Fundamental Theorem of Calculus ?

Q: Use the Fundamental Theorem of Calculus to evaluate the following definite integral:

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Q: use linear approximation to estimate the value of 1.1^1.327

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Q: Evaluate the integral. 1//3 2-1 tA - 1 8 dt

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Q: Proves/1=L2

A: The given figure is

Q: L In(t?)dt **csctdt dx -8

A: Given:  1. ddx∫x9lnt2dt2. ddx∫4x2 -xcsctdt3.∫18x43dt To evaluate 1,2,3 using Fundamental theorem of…

Q: (x²-3x+1) dx

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

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: (6x5+2x) dx

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Q: (b) dx

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Q: 4. Compute f'dr by using fundamental theorem of integral calculus.

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Q: Use The Fundamental Theorm of Calculus.

A: Derivative of the function f(x) is the measure of how fast the value of function changes when the…

Q: Use the fundamental theorem of calculus part 2 to evaluate the integral: 2 dr Note: Round to the…

A: Evaluate the integral using Fundamental Theorem of Calculus Part 2 : ∫169xdx

Q: What was the most important thing you learned during the class discussion?  Reflection about…

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Q: In at least 4 sentences, write what you have learned in Fundamental Theorem of Calculus and Definite…

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Q: rV4- a² dx

A: Let's find.

Q: 188. dt 3 .2

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Q: Use the definite integral and the Fundamental Theorem of Calculus to solve the following problem. If…

A: Surface area of cube = 6a2 square units Now,              Fundamental Theorem Of Calculus states…

Q: Evaluate J3 25-x² 2x3 dx. Show complete pencil-and-paper calculus-based evidence for your…

A: We have to evaluate the integral ∫342x325-x2dx.

Q: When are the two versions of Fundamental Theorem of Calculus helpfu

A: The first version of the fundamental theorem of calculus involves a variable like x so this will…

Q: State the first part of the Fundamental Theorem of Calculus (FTC).

A: The first part of fundamental theorem of calculus states that -

Q: find the derivative.

A: We know that , if Then, by Second Fundamental theorem of calculus, we have

Q: (3x² + 5x-2) dx

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Q: Evaluate the integral using the Fundamental Theorem of Calculus. xp

A: Given that a finite integration and we find the value of this using fundamental theorem of calculas.…

Q: Evaluate the integral. | Vx? + 2xdx

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Q: This is a multivariable calculus problem. Show that quaternion multiplication is not commutative.…

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Q: 2x* dx

A: Here is the solution

Q: 9. Demonstrate the method of the Fundamental Theorem of Calculus to find the following definite…

A: our objective is to find the definite integral.

Q: Evaluate the following definite integrals using the Fundamental Theorem of Calculus:

A: The given two integrals are:a∫-552xx2+2dxb∫01x3+1x+1dxFundamental Theorem of Calculus says:If Fx is…

Q: 1. Show that dr

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Q: (- 00 ,a) is measurable.

A: Given a statement

Q: How was the birth calculus attained?

A: Calculus was borned, rather developed independently by Newton and Leibniz, this marked as one of the…

Q: Use relevant definition(s) and theorem(s) to prove the fundamental theorem of calculus part 1.

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Q: Using the Fundamental Theorem of Calculus, we know that 1 dx x2 3 is equal to...

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Q: Explain in your own words what the Fundamental Theorem of Calculus says. Be sure to address both…

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Q: Discuss the two versions of the fundamental theorem of calculus

A: This the problem of Real Analysis, Theory of Reimann Integration.

Q: Evaluate J 4x° – 2x + 7x – 4dx -

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Q: where are used calculus?

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Q: 8. Ssin(1 – Int)dt

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Q: 5. What is the car's acceleration when they meet? Make sure to show work for this answer using…

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Q: Vx3 (х + 5)dx.

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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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Q: Evaluate J12dy

A: Solution )∫12dy We know that by the integral formula ∫a.dy = a∫dy And ∫dy = y So ∫12dy = 12∫dy…