Find the polynomial p(t) = t + azt² + a,t + a, for which the integral J = has the smallest value.

Q: Use the fundamental theorem of calculus part 2 to evaluate the 3 integral: S (9x – 4) dæ. -2

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

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Q: Use a fourth-degree Taylor polynomial centered at 0 to approximate the integral from 0 to 1,…

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Q: Use the specified substitution to find or evaluate the integral.

A: We need to use the specified substitution to find or evaluate the integral.

Q: Find the general integral and compute 3 diferent solutions for : xzx+(x+z)zy=y-x

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Q: Evaluate the integral f 2x (x² + 6)° dx using the substitution u = x2 + 6. | 20(x² + 6)* dzx +C

A: In this question, the concept of Integration is applied. Integration Integration is a method of…

Q: Show that Q(i) is an integral domain

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Q: By the odd extension method applied to the function f (x) = e¯2x, wherex > 0, the Fourier integral…

A: Given the function  fx=e-2x

Q: Evaluate the integral: Jxe dx хе -2x -xe -Xe 2x +C -Xe2x e -2х —хе +C 4 Xe 2: -2x хе -2x e +C -2x…

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Q: Find the complete, singular and general integrals of p3 + q3 = 27z. %3D

A: We have to find the complete, singular, and general integrals of:  p3+q3=27z

Q: xdx J Væ +3

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Q: Evaluate the integral. 3t2 k dt 1 + t2' 1 + t3

A: We have to find integral

Q: Find the complete integral of the z'(p°z² +q°)=1

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Q: Find the total differential z = 2x3y − 8xy4

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Q: Evaluate the integral of (t2) / √(1+t2 )with respect to t.

A: It is given that, f(t)=t21+t2 It is known that, ∫1(x2+a2)dx=logx+x2+a2+c and…

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: dx 2 -o x+4x+5

A: The general form of a complex number is given by , where a, b are two real numbers and . Any complex…

Q: Evaluate fv*+1dx x2 A. 를 (1 +즐)를 -를 (1+ 즐)를 :. 를 (1-즐)를 -를 (1-2)를 + C + C + C D. + C Evaluate the…

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Q: The improper integral 2dx 0. 1-x2 3 T

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Q: Evaluate the integral. dt V 4 + t2

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Q: Find the fourth Taylor polynomial for f(x) = Vx centered at 1 and use it to estimate V1.4

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Q: Evaluate the integral f 2x (x2 + 7)° dx using the substitution u = x2 + 7. 2.x (x² + 7)° dx +C

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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: Evaluate the integral | t(sec t2)4 dt

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Q: Evaluate the integral f 2x (x² + 3)° dx using the substitution u = x2 + 3.

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Q: What is the 1st-order Taylor polynomial of: f(x,y) = e(x+y) -1 at (0,0)

A: Explanation of the answer is as follows

Q: Evaluate the integral. integral t e -3t dt

A: Let given integral be - y = ∫t e-3tdtUsing by parts to integrate the above integral - ∫uv dx = u∫v…

Q: Evaluate the integral 35 dz 4 by making the substitution u = x* – 6. +C

A: integration

Q: Find the integration distance (f, 9) = | f(x)g(x) dæ between the given polynomials. f(x) = 11æ – 3,…

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Q: Find the solution in the form of Fourier integrals: U₁-3 = 0, uz (0, t) = 0, |u(x, t) bounded as…

A: We have the following partial differential equation : ut - 3uxx = 0  , x,t > 0 With boundary…

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

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Q: Solve using the bisection method f(x) = e-x* – 2x + 1 starting at the interval [0.75,1]

A: Consider the provided question, We have to solve the given function by using the bisection method,

Q: Find the complete integral of (p2 + q2)y = qz.

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

A: π

Q: Find the integration inner product on C[–4, 1] of the given functions. f(x) = 15x g(z) = 3r* (f, 9)…

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Q: Q2/Evaluated the integrals v2 1- f– (1-v2 )2

A: The integration of v2/(1-v2)5/2.

Q: Use the local linear approximation of (1 – x)2º at xo O to estimate (0.99)2º. %3D

A: The linear approximation of f(x) at x0 is given by L(x) = f(x0) + f'(x0) (x-x0)

Q: Use a sixth-degree Taylor polynomial centered at zero to approximate the integral. Function…

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

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Q: Evaluate the integrals ∫(t + 1)2 - 1/t4 dt

A: To evaluate the integral: ∫t+12-1t4dt Evaluating the given integral.…

Q: Determine the first three nonzero terms in the Taylor Polynomial approximation for y'=cos y + e2x…

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Q: Evaluate the integral dx (2x + 4)* by making the appropriate substitution: u = dx (2x + 4)°

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Q: Compute the second degree Taylor polynomial at point (0,0) of the function f(x,y)=er*)

A: Given: fx,y=e-x2+y2

Q: Find the integration inner product on C[–4, 2] of the given functions. f(x) = 15x g(x) = 2x³ %3D…

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Q: Evaluate the integral. dx i. 2 x²Vx2–1°

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Q: Expand, that is, perform the indicated operations on the differential operator D. 1. xD(R+ x)

A: Given that         xD(D+x)  Here we have to expand this and perform the indicated operations on the…

Q: Evaluate the integral. ' 2 (8t i – t³ j + 2t³ k) dt Jo

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Q: 2t + 1 What is the indefinite integral of dt t3 -8t + 21t – 18

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