Part IV: Find the following definite integrals using the First Fundamental Theorem of Calculus. 12)S(2 - > ) dt

Q: Prove that 1 + p'2 p4 where primes denote differentiation with respect to 's'. 1. x"2 + y"2 + z"2 %D

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Q: Use Part 2 of the Fundamental Theorem of Calculus to evaluate the definite integral. a) S(1 + 3x –…

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

Q: The value of the definite integral' f(x )dx for f(x) = 3 is:

A: We are going to evaluate the value of the given definite integral for f(x)=3

Q: Evaluate the definite integral. sin(3t)dt

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Q: Evaluate the integrals ∫√t sin (2t3/2) dt

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Q: In this problem, you are asked to carefully read Example 6.4.2 of APEX Calculus. 1 The given…

A: An integral is given by, ∫15+x2dx. The objective is to find the correct substitution which is to be…

Q: S(2- sec2x) elmale sec³x sec(3A – x) e ln (xle) What should be the value of A for dr to be…

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Q: Evaluate the integral •5 sin(t)dt 6.

A: Given:∫65sintdt

Q: Use the Fundamental Theorem of Calculus to evaluate the following definite integral. | (4x2 + 9) dx…

A: To find the value of definite integral using  fundamental theorem of calculus.

Q: Use the Fundamental Theorem of Calculus to evaluate the following definite integral. 8 3 dt t 1

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Q: 7/2 2. Is cot x dx an improper integral? Explain.

A: Given integral is not an improper integral.

Q: Evaluate the definite integral. sin(2t)dt

A: We will solve the following.

Q: Use the Fundamental Theorem of Calculus to evaluate the following definite integral. V3 2 8 dx V1-x?

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Q: 17. Why doesn't the definite integral 1-x² dx make sense? (Hint: Think about domains.)

A: To find: The reason why the definite integral ∫231-x2dx does not make sense. Explanation: Substitute…

Q: Evaluate the definite integral. t(5 – t)² dt

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

A: Use fundamental theorem of calculus

Q: 27. tan'x sec x dx 30. tan r dt

A: the basic formulae must to solve these problems: 1) ∫xn dx =xn+1n+1+c2)d tan(x)dx= sec2(x) 3) d…

Q: integral from 1 to 2 of (e1/x^3 ) / x4

A: To evaluate

Q: Evaluate the following definite integral using Calculus: 2 (3x² +1)dx -2 3.

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Q: 2 X+2| dx -3

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Q: Evaluate the definite integral. 6.³ sin(3t)dt

A: The given integral is Sin(3t), limit from 0 to pi/3.

Q: Q16: Find the indefinite integral: (e' + tº) dt

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Q: Use Part 1 of the Fundamental Theorem of Calculus (and properties of definite integrals and the…

A: Solve the following

Q: b) Evaluate the integrals using Part 1 of the Fundamental Theorem of Calculus. 2. L, 4x(1 – x²)dx…

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Q: 4. Evaluate the definite integral_ TC 3. sin(3t) dt 0.

A: Explained below

Q: - Using the integral definition of gamma function show that T(7) = 61(6)

A: Integral definition of gamma function is Tx=∫0∞tx-1e-tdt . Put x=7 in Tx=∫0∞tx-1e-tdx and simplify…

Q: Question Eight:- Evaluate the 20 points following integral sinx d²y 2t2 dt dx2 In x Your answer

A: on using leibnitz rule.

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: QUESTION 3 a) Evaluate the integral tanh (2x)sech (2x)dx.

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Q: Find the indefinite integral

A: Given: ∫t1-t4dt

Q: (ii) Hence, by using Leibniz Rule for Differentiation Under the Integral Sign, compute the value of…

A: Leibniz Rule for Differentiation under integral sign:- ∂∂t∫atbtfx, tdx=∫atbt∂f∂tdx   + fbt, t∂bt∂t-…

Q: Sin (x-t) u(t) dt = 1- Cos x

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Q: Evaluate the definite integral. sin(4t)dt

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Q: 6) Use the successive approximations method to solve the following Volterra integral equation: 2 и…

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Q: Evaluate the definite integral 27 3 16 sin (x)dx using Part 1 of the Fundamental Theorem of…

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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: L (x − 3)(x + 2) dx – -2

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Q: Evaluate the definite integral. /3 sin(3t)dt

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Q: 3. Find the derivatives of the following in two ways: -by evaluating the integral and…

A: Here we solve this Question by  First integral and find derivative  By first fundamental theorem of…

Q: dx S x2 ( 4. x²+x+1)

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Q: Evaluate the definite integral. ' sin(4t)dt 1/2

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Q: Use the Fundamental Theorem of Calculus to evaluate the following definite integral. 8 e 2x dx…

A: The given definite integral,         ∫028 e2xdx

Q: Find the indefinite integral. Solution in handwritten b. f(x+1)√2- xdx

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Q: 8. Evaluate each definite integral using the Fundamental Theorem of Calculus, Part 2. Ľ³…

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Q: Evaluate the definite integral. 4 cos(xt/2) dt

A: We need to evaluate the following integral. So,            ∫014cosπt2dt=4·∫01cosπt2dtLet…

Q: Question 3: Find the integrali(using u-substitution) Ses (8x+1) dx

A: To evaluate: I=∫cos (8x+1) dx

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

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Q: Question 2: Use the Green's theorem to solve $(v² +3x² \dx+2xdy which bounded by x=0,y=0 and 4(x² +…

A: We find the given integral by using Green's theorem.

Q: Evaluate the definite integral. integral (lower 0, upper 3) t^3 sin(t^4) dt  =

A: We have to solve the definite integral

Q: 4. Use definition (not tables) of L{f(t)}= [ e"f(t)dt to find L{sin(2t)} .

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