1.) Give all the complete and derived formulas of Differential Calculus. 2.) Give all the complete and derived formulas of Integral Calculus.

Q: ,2 2. 6+t dt

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Q: 14. Evaluate the integral: | ze dz. 1

A: Integrating by parts.

Q: Find a linear differential operator that annihilates the given function. (Use D for the differential…

A: A linear differential operator g D is called    annihilates the functions fx if and only if…

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

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

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Q: List of formula for Integral calculus

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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: The basic idea of optimization is that we have a quantity (represented by a function), and we need…

A: The basic idea of optimization is to find the maximum or minimum of a function using the different…

Q: A defense contractor is starting production on a new missile control system. On the basis of data…

A: the given rate of labor use is  the given lower and upper limit is

Q: The integral from 2 to infinity of 6/((x+5)^(3/2))

A: ∫2∞6x+532

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

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Q: -25 Evaluate the integral: dax x²Vx2 +25

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Q: Did Charles Babbage used calculus (integration) in inventing computer?

A: Yes

Q: Evaluate the definite integral exactly, using the Fundamental Theorem. 6. 1 -dt 1 dt II

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Q: 2. Use the fundamental theorem of calculus part 2 to compute the integral 1° dr. 0,

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Q: 4.3 Use the calculus of residues to evaluate the following integral (x2- dr. + 1)2

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Q: The value of the triple integral 0. 0. is

A: Evaluate:

Q: 2. F(x) = [ cosr' dt

A: Use fundamental theorem of calculus

Q: id I prove this qa is not to zero correctly? Please look over my proof and qa is not equa

A: Proof by contradiction:  Argument by contradiction is a type of proof in logic and mathematics that…

Q: Evaluate the definite integral 3 2 sin (2)dx using Part 1 of the Fundamental Theorem of Calculus. 57…

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Q: „T/2 sinOdo 183.

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Q: 6. Evaluate the fallowing real integrals by residue theerem 3 2计 I = Ssine -d8;a>l anse 2(a- Ja?1)

A: Given: I=∫02πsin2θa+cosθdθ, a>1

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: 4. Express f(x) by the Fourier integral where f(x)= (-2, -3< x < 3 otherwise.

A:

Q: rV4- a² dx

A: Let's find.

Q: 188. dt 3 .2

A:

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: Write some important things about integral calculus

A: Given: The important thing about Integral Calculus:

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: Explain why the two forms of Green’s Theorem are analogs of theFundamental Theorem of Calculus.

A:

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

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

Q: The nth root of a number can be approximated by the recursive formula R. k+1 A == ((n-1)R+ (R) n-1…

A: Given that,The nth root of a number can be approximated bythe recursive…

Q: x4/3' dx -1 | --

A:

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

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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: How is integral calculus related to differential calculus?

A: Solution

Q: By the Fundamental Theorem of Calculus 2+x² Newton-Leibnitz, Theorem) evaluate √x dx

A: We have to evaluate  the given integral  ∫142+x2xdx  by using fundamental theorem of calculus.

Q: Express limn→∞∑i=1nsinxiΔxlimn→∞∑i=1nsin⁡xiΔx as a definite integral on the interval [0,π][0,π].

A:

Q: Find a linear differential operator that annihilates the given function. (Use D for the differential…

A: See the detailed solution below.

Q: Use the Fundamental Theorem of Calculus Part II to compute 0. 4 sec (x) dr.

A: Proceed as shown below

Q: du

A:

Q: 27 Use the Fundamental Theorem of Calculus to evaluate S (Vx2 -) dx. 8.

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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: PitgXL

A: We will use the fundamental theorem of integral calculus and the Newton-Leibnitz theorem to find the…

Q: Evaluate J 4x° – 2x + 7x – 4dx -

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Q: What is differential calculus? And what is the best example to understand it?

A: Differential calculus: Differential calculus is subfield of calculus. In the calculus it has two…

Q: Evaluate +he Integrali brit

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Q: The side if a square floor tile is measured to be 4 inches, with a possible error if 1/32 inch. use…

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Q: Use the Definition of a Definite Integral or Theorem 4 from Section 5.2 to find the exact value of…

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Q: 8. Ssin(1 – Int)dt

A: