Demonstrate that x' + 3x – 8 is irreducible over Q. -

Q: evaluate the integral. li+4/ij-8r³/2k)dt

A: To evaluate the integral, ∫14t-1i +4tj-8t32kdt

Q: Evaluate the integral. 2 dt 1- t2 V

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Q: Evaluate the integral. 7y 1-7y dy

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Q: Evaluate the integral 5a2 - x+27 da. (x2 +9) 5x3 x2 + 27z) · In|r(x² + 9)|+ C 2 3 In |피 + 2z In |2…

A: Topic - indefinite integration  Note- as per our guideline if more than one question uploaded only…

Q: Given that f xdx = 1/2 and f²dx = compute the integral [*(1-x)²dx.

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Q: In x Evaluate the improper integral dx 1 Divergent -In 2 4 in 2

A: To evaluate: The improper integral ∫1∞ lnxxdx. Calculation: First find the integration of the…

Q: what is the integral of e^(-2a|t|) from -w to w?

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Q: Evaluate the integral. In(9 x - 8) dx =| +C %3D

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Q: Evaluate the integral. 了學 ( Inx dx O- In x - +C 2x 4x2 O-4 In x - + C 4x2 0.을 Inx- +C 2x2

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Q: Evaluate the integral +2 zp; :- 2 in the two cases: 1) y = {z :|2| = 1}; 2) y = {z : |2| = 3}.

A: We will evaluate it by Cauchy Residue Theorem Let R be the residue then ∫f(z) dz = 2π i R Firstly,…

Q: F[x₁,...,n] is an integral domain.

A: Solution:-

Q: 4 – dt 2 cos 4t 1.

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Q: Compute f'cx) of ×そ9 O f(x)- X-3 at X, = 3 の f(x)= x*+ ラメ+ タメ+1 at Xo=-2 f(x)= 4cos x + 2 sinx at X=…

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Q: 2 dt 4+ t²

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Q: D (x) is not integrable on [0,1]

A: Note: Here we are solving 1st problem for the next problem please submit the question again. Given:…

Q: Evaluate the integral. (1s - t )dt t + 8 -2

A: Given that the integral is ∫-2016t5+18t4-tdt. It is known that ∫xndx=xn+1n+1+C.

Q: Find the local linear approximation of f(x) = In(5 + x) at xo = -4. %3D In(5 + x)

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Q: 2. Use Cauchy's Integral formula, Evaluate the following • I= sin4z ,IZl= 3

A: I am attaching image so that you understand each and every step.

Q: y = sech*x = In(_+ V1- x², sechx = In(- 1+ V1-x² Prove that .... ..

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Q: Explain Bessel equation and Prove that 2 (n + 4)Jn+4x (i) (ii) In+3X + Jn+5X = 4J"n = Jn-2 – 2Jn +…

A: The objective is to explain Bessel equation and prove that  (i) Jn+3x+Jn+5x=2xn+4Jn+4x (ii)…

Q: Find the indefinite integral. 4x2+2x-1 d.x none of these Omz + 1| -31m|z미-글+C o+ Inz* + =*|+C In a+1…

A: Given: I=∫4x2+2x-1x3+x2dx   We know that; The Power rule: ∫ax+bndx=ax+bn+1an+1+C ; n≠-1 And…

Q: Prove the irrationality of n² by expressing the integral In - = 6.² P(x) sin x dx as a linear…

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Q: 7. Evaluate the integral r8-2x (x + y + 1)-2 dydr.

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Q: The improper integral 2dx is 1-x2 0.

A: π

Q: 7. Use the Fundamental Theorem of Line Integrals to evaluate S(6xy, 3x² + 6y²) · dr where C is any…

A: Line integral theorem

Q: Evaluate the integral. dt 5 4t | X

A: Refer to the question.The provided definite integral is as,

Q: Consider the integral 2 6z² In(z) dz

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Q: Show that A and AT have the same nonzero singular values. How are their singular value…

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Q: Evaluate the integral. 4,3 - 32+ 4 른t) dt

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Q: Evaluate the improper integral t* e-2t 3+e-4t at

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Q: Evaluate the integral. 4 2t 9 -i- j+¬Vt k dt (9+?)*

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Q: Evaluate the indefinite integral. 7dx a In(3x) +C

A: We hae to evaluate  the indefinite  integral.

Q: Find the Selution of (1-t +3t)4 (t) di - , (2) In which IL) denoter Bessel function

A: Leibniz integral rule : ddx∫bxaxFtdt=∫bxax∂∂xFtdt+Faxddxax-Fbxddxbx   Linear Volterra Equation of…

Q: The integral x²/4 - x²dx can be determined using the substitution 4- x2 = t.

A: Given integral: ∫02x24-x2dx

Q: Explain Bessel equation and Prove that 2 (i) (ii) In+3X + Jn+5X =÷(n+ 4)Jn+4x 4J"n = Jn-2 – 2Jn +…

A: Definition Bessel's Equation: The differential equation x2d2ydx2+xdydx+x2-n2y=0 where n is a…

Q: 8. S(1- sec3x)²dx

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Q: . Show that 1, x, x² are three particular integrals of x (x2 - 1) yı +

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Q: What is the integrable form of dr? 1 -1) du -u?) 2 du 2022-01..

A: Find the integrable form by substitution method

Q: Evaluate the integral: Sen(+²+2x-7) ox dx A x² + 5x + In|3x-6|+C B +5x+31n|x-2|+C X + +In|3x-6|+C Ⓒ…

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Q: 18. Show that Ein d(k)³ = (Ekin d(k))² for all positive intege m

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Q: In x + In(x – 1) = 10 In(x + 25) – In(x – 1) = 3 e2x – 2ex = 15 e2x – ex – 12 = Q %3D %3D -

A: i) ln x+ln(x-1)=10ii) ln(x+25)-ln(x-1)=3iii) e2x-2ex=15 Note:      Multiple part question are given,…

Q: Evaluate the iterated double integral. I 3 3y be dady A

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Q: D Find a singular saluhion of DE: %3D

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Q: 3 In 3x Evaluate the defınite integral : J 6x2

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Q: Evaluate the integral. to dt 5/2 x2 (x² – 16}"-

A: Given:  ∫ x2 dxx2 -1652 =?Using Substittution Method:…

Q: Evaluate the improper integral .a-2 dz. 1 dr. (4-a)2

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