Use the fact that x'-6x = 2 has no integer solution to prove there do not exist 3 consecutive integers k – 1, k, k + 1, such that the cube of the largest is equal to the sum of the cubes of the other two.

Q: Evaluate the indefinite integral. -2.5 -6t -8t -1) dt %3D 61-25 -8t-1) 8t 1) dt%3D 19-

A: To determine the value of the integral.

Q: x² + x – 2 (3x – 1)(x² + 1)

A:

Q: (22-4) (교3-4z)3 dz

A:

Q: 5. Find the indefinite integral 6.x²dx (2x³ + 7)3/2

A: The solution for the above question is as shown below.

Q: The number of iterations necessary to solve f(x) = x² – 6x + 5 in [0 ,4] using the bisection method…

A:

Q: Find the indefinite integral: 30 [cos 3x + sin 2x + e5x]dx 10sin 3x -20 cos 2x +6 e5x + C O 90sin 3x…

A:

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

A:

Q: Sæ² 1 + x²dx

A:

Q: ) show that 2n" + 1 1+ 222 2n t hence %3D n (n² + 1) 2n4 +1 by first expressing evaluate integrand…

A:

Q: find a complete integral of q=3p2

A: Given that : q=3p2 It can be written of the form ,3p2-q=0                              ⋯1 Since 1 is…

Q: 7) Solve for x: In(x + 3) = In(2x) %3D

A: The given equation is lnx+3=ln2x.

Q: 2.x D' -8 .

A:

Q: Find the positive root in 4th iteration of the equation xeX-3 in the interval [1,2] using Regula…

A: We have to find the positive root in the 4th iteration of the given equation in the interval 1,2…

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 Bisection method to find the solution accurate to within 10-5 for 2x cos (2x)-(x+1)230on…

A:

Q: Evaluate the Integral 2. S V5 + 12x – 9x²dx - ANSWER: 2. (3x-2)v5+12x-9x²+9Sin¬13*- 2]+C (3х-2)

A:

Q: Use any method to evaluate the integral. 4 - 4-X xp- 4X + 4-X

A:

Q: The number of iterations necessary to solve f(x) = x² – 6r +5 in [0,4] using the bisection method…

A:

Q: Find a general solution of each reducible second-order differ- ential equation y" = 2yy'

A: Recall the chain rule of calculus:

Q: (i) Find the Cauchy principal value of the integral dr. +4z + 8

A: The objective is to find the Cauchy principal value of the integral ∫-∞∞xcosxx2+4x+8dx

Q: Find the definite integral from 3 to 5 of x+2 / (x^2 - 2x) using partial fraction decomposition

A:

Q: Evaluate the Integral / tanh (2x)đx. A @ --n|cosh(2x)| + C B -In|cosh(2x)| + C © 21n|cosh(2x)|+ C D…

A:

Q: 1. Evaluate the integral [(4z° +3z2 +2z– 6) dz

A:

Q: The integral 15x* - x* - 43x – 19 (x + 1)2(x2 – 6x + 13) can be rewritten as

A:

Q: Find the number of positive integers less than 1000 that can be expressed as the difference of two…

A: Find the number of positive integers less than 1000 that can be expressed as the difference of two…

Q: Show that 3x2 +6x +2 = 3 (x+1) - by completing the square. Hence, evaluate the 2 integral dx. V3x? +…

A:

Q: 1. Use the Table of Integrals in the back of your textbook to evaluate ∫11dx/x^2√16x^2+36 a.Perform…

A:

Q: Find the integral of f(3x2 + 4x + 1)*(3x + 2)

A:

Q: Using decomposition into partial fractions, the following integral is equal to s 27 2x + 1 3x3 - 27x…

A:

Q: Find the general solution to the DE using the method of Variation of Parameters: у" - Зу" + Зу'…

A:

Q: Solve the following PDE: Ut = Uzz + Uz -∞ 0 subject to ze initial condition u(x,0) = f(x) Show all…

A: As per the question we have to solve the following partial differential equation : ut = uxx + ux…

Q: Express f(x) = x2 / x2+4 into partial fractions and hence show that ∫02f(x) dx = 2 - π/2.

A:

Q: Evaluate the integral

A: ∫xndx=xn+1n+1+C

Q: The integral from negative infinity to 1 of 8/((2x-3)^2)

A: Given         ∫-∞182x-32dx

Q: 1 x²(x3 - 4)³ of xp

A:

Q: Q.x2(x2+1)y′′+7xexy′+9(1+tanx)y =0

A:

Q: Find the indefinite integral J(-16r² – 4x + 6)dr. a. -12r-4x + 6r +C b. -4x*- 2r+ áx +c c. -4x-2r+…

A: Solve the following

Q: 1. What should be A for the path independent of (2,4) xy + A 2Ay – x + xp- y? fip- (1,2) Moreover…

A: According to the given information, it is required to find the value of  so that the below integral…

Q: – 30 - Evaluate the integral: -d.x x2 Vx2 + 16

A:

Q: Solve the following DE using Separable method. 2y' = x(1- y')

A:

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 Ⓒ…

A:

Q: 2. Use the Table of Integrals in the back of your textbook to evaluate ∫11dx/x^2√16x^2+36 a.Perform…

A: While solving this indefinite integral, we need substitutions twice.

Q: Find the interval and radius of conv. of In(1 – x²)

A: The power series representation of given function ln1-x2 is given by: ln1-x2=∑n=1∞-x2nn

Q: Find the indefinite integral. Vx +8 xp- 3 7 2 Vx +8 6 6 4 3 - X- 35 + + C X- .3 15

A:

Q: b) Show that 2x2 +8x +14 2(x+2) +3 by completing the square. Hence, evaluate the integral dx. (x…

A: Given that: ∫3(x+2)2x2+8x+14dx

Q: Express the integrand as a sum of partial fractions and evaluate the integrals ∫ 1/ x^3/2-√x dx…

A: Given:∫dxx3/2-x1/2

Q: 4. Evaluate the integral: /2 2x 1/4 /1. V4 V1- x²

A:

Q: Evaluate the integral: –(9z²+7x) dr %3D (1-1)(z+1)²

A: Given :∫-(9x2+7x)(x-1)(x+1)2dx

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.