If n^2+6n+11 = x^2+y^2 for positive integer n, x and y prove [xy/2] is composite. Note: [t] represents the greatest integer less than or equal to t.

Q: Compute the integral ∫xdx/1+x4.

A: Let,

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Q: Evaluate the following integral. 4 5х - 1 dp- x+ 1

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Q: Evaluate the integral. '3 dt 1

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Q: Find all exact sdutions on [o,2T] (Gnter your 90swer in a comma seperated list tan (x)-25itan(x)= 0

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Q: 28. Evaluate the integral. x5-5x+4 x2

A: Indefinite integral: - The term "indefinite integral" refers to an integral that has no upper or…

Q: If the interval [4, 18] is partitioned into n = 28 subintervals of equal length, what is Δx?

A: Total length of [4,18] is (18-4)=14  Given that, n= number of partitions= 28

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

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Q: 6dx x - √ S 3√x²

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Q: Evaluate the integral: */64 – a°dz .3 2 -

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Q: 14. Find the indefinite integral. 49x7 13-7x8 lal 13– 72 |+C a. b. In| 13-7x |+C c. 911n| 13- 7 |+C…

A: Assume u=-7x^8 Find du

Q: problem in photo attached

A: Take the constant out of the integral sign. Simplify the expression  as x1/3

Q: Evaluate the indefinite integral S(z -9-dz 를-9z + 듣 +C 4x4 중-9z + + C 222 - 9x + 7lnx³ + C - 7 9x -…

A: First we write each term using exponent

Q: 14. Find the indefinite integral. 7 49x xp- 13-7x8

A: Given integral is

Q: S |8:xydxdy y=-2 x=1

A: For the following problem,

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: 1. Show that cosh 4x = 8cosh“x - 8cosh? x + 1 .

A: Given problem:- Show that cosh(4x) = 8cosh4x - 8cosh2x + 1

Q: a) Determine the number M and the interval width h so that the Composite Simpson Rule for 2M…

A: The formula for the composite Simpson's rule is . The error in the composite Simpson's rule can be…

Q: 1.al If 123x 78425167 is a muitiple of 1l, tind x.

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Q: Evaluate the definite integral. '1 3 + 7t³j+ Vik) dt /-1

A: Consider the given definite integral

Q: Compute the integral ∫ xdx / √5+x−x2.

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Q: 1. Evaluate the integral

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Q: Evaluate the integral: Sen(1²2+3x-7) е dx A x² + 5x+In 3x-6|+C XZ B +5x+31n|x-2|+C 2 C x ²2+ = +…

A: On solving this we will get

Q: Prove that In (1tx) Lx for without using the value the orem. mean

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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: Evaluate the integral " -2n 1+4cost dt. 17-8cost

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Q: The value of The binary integral is dxdy Luherea andb positive 80 -xy real constants) be

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Q: хах 9. S 1-x8

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Q: 2. Evaluate the indefinite integral. 8dx xln(2x)

A: topic - indefinite integral

Q: Compute the integral ∫xdx / √5−x2.

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Q: 2°) Use integration by parts to prove that, for any positive integer n, (2n + 1) In = 2n In-1. 3°)…

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

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Q: 23+dt (4+3 Co+ 3+)5

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Q: 13 1 (1+2x)?

A: We have to integrate the given integral

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

A: Given integral: ∫02x24-x2dx

Q: 6. S21-2xdx

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Q: 17. Evaluate the integral. n x)²dx

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Q: the infinite integral of 3x^4-2x^3+6x^2+23x+7/x^2-2x+5

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Q: Evaluate the integral. '5 (In(x))² xp x3

A: Given integral

Q: In 8x Evaluate the definite integral : S dx 5x4

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Q: Express x8. -x over Q[æ] and over F2[x] as a product of irreducible

A: Let f(x) = x8 — x. Over Q,f(x) = x(x7 — 1) = xϕ1xϕ7x=xx-11+x+...+x6 Note that  ϕ1x and ϕ7x are…

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

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

Q: Jx (2х — 3)%ӑх

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Q: Suppose we perform the substitution .3 u=9-x in the integral

A: Given that:∫123x29-x3dx