Suppose that ≺D,+,⋅≻ is a well-ordered integral domain. Then the least positive element in D is the unity e∈D, since if a∈Dp such that e>a, then e−a∈Dp⟹a(e−a)∈Dp⟹a−a2∈Dp. I.

Q: 30 +4) de 3e+ )

A:

Q: 12) -5Vx 2 + + 6Vx) dx 3 11х A) + C 3 2 1 1 3 3 В) -Зх° + 2х° + 5х° + C 4 6 3 5 С) -3х° + 2х* + 5х°…

A:

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: 7 N 3 + -4√2 + √z dz

A:

Q: Prove without calculating the integrals explicitly that V1 + x³dx < | V1 + x²dx

A:

Q: Suppose X ∼ Binom(n, p). Show that E[X] = np.

A: Suppose Its probability mass function is defined as,Where,

Q: 4 5y²-8X+6) dx =?

A: To evaluate the given definite integral

Q: 5. Show that if a, b, c € R, where R is an integral domain. Show that if a ‡ 0 and ab = ac, then b =…

A:

Q: Suppose that a and b belong to an integral domain and b ≠ 0. Showthat &lt;ab&gt; is a proper subset…

A: Let R be an integral domain. A commutative ring R is said to be an integral domain if non zero…

Q: Evaluate the integral. f(3x + (3x + 7)² dx

A:

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: In an integral domain, show that a and b are associates if and only if&lt;a&gt; = &lt;b&gt;.

A:

Q: The PG(2, q) has 133 points. Find algebraically the value of q in PG(2, q). Note that q is the…

A:

Q: Evaluate the integral of fx³dydx

A:

Q: Why can we pull the 2 out front and change the bounds of the integral from -2 to 2 to 0 to 2…

A: Substitute y^2=u then integrate with respect to u

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

A: Given function is fx=x3+3x2−8 We have to show that fx=x3+3x2−8 is irreducible over Q(Rational…

Q: Evaluate the integral J7x-5)² +5

A:

Q: Show that the characteristic of an integral domain D is either 0 or a prime p.

A: We want to prove that the characteristic of an integral domain D is either 0 or a…

Q: prove that (z(square root 2,+,×)) is integral domain.

A: We have , ℤ2   =  a + b2 / a , b ∈ ℤ We need to show that  , ℤ2 is integral domain. We know that , a…

Q: 응 +-름구 + 4z +C

A:

Q: Evaluate the integrals

A: Given information: ∫141ti+15-tj+12tkdt