2. Prove or disprove that Z, xZ, is integral domain.

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

A:

Q: 1+x a) (-x² + 2y) dydx; 0. x2

A:

Q: Evaluate the integral ∫1/ √tcos (√t+3)dt

A:

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

A:

Q: use a computer algebra system to evaluate the triple iterated integral.

A: Using a calculator we get:

Q: 22. Evaluate the iterated integral. (b) f. [, 2x + »)'dy (a) x+y+ xy dydx

A: Now we will solve the given double integral  We know integration of Xn dx = X(n+1) / (n+1) + C ,…

Q: use a computer algebra system to evaluate the triple iterated integral.

A: We have given a triple integral;

Q: Evaluate the integral of 3dx/(2x^2 + 4) from 0 to 0.2 *

A:

Q: - Evaluate the iterated integral 3xyz dz dy dz.

A: Definition. • In calculus, an iterated integral is the result of applying. integrals to a function…

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

A:

Q: Verify the Green's Theorem to evaluate the line integral . (2y²dx + 3xdy),

A:

Q: 2. Use Cauchy's Integral formula, Evalnate the following. • I= 6 Sin4Z :(Z-4)3 IZ1= 3 I = . tanttz…

A: Given

Q: prove by definition that the integral from a to b of xdx = b^2-a^2/2

A: To Prove:    ∫abxdx=b2-a22

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

A:

Q: Use the Fundamental Theorem of Calculus to evaluate the following definite integral. 2 dt 3 2 dt = 1…

A:

Q: 2. In r dr

A:

Q: SVA- 4-y² √8-x²-y2² z² dzdxdy. √x²+y²

A:

Q: n. b) 2e u+2 dydz. 0 Ji

A:

Q: Use Green's Theorem to evaluate the integral 3x²y²dx + (5y³ – x³y²)dy, C

A:

Q: Is dz

A:

Q: F[x₁,...,n] is an integral domain.

A: Solution:-

Q: Evaluate the integral. 7t dt 1 + t2' 1 + t2

A:

Q: 2 dt 4+ t²

A:

Q: Show that y^3dx+3xy^2dy=0 is separable and exact

A:

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.

A: Given:            ∫461t2-9dt

Q: Prove that (Z(sqrt(2)), +, ×) is an integral domain.

A: We know that , ℤ2 = a + b2 / a , b∈ℤ . Clearly , ℤ2 forms a ring. We know that , a commutative ring…

Q: 15. Evaluate the integral zVx² + y²dzdxdy by using cylindirical coordinates.

A: I have Provided this answer in step-2.

Q: Prove the following statements for arbitrary elements x, y, z of an ordered integral domain D. If x…

A: Consider the given information. If x > 0 and xy > 0 Let's take y<0 than y will be negative.…

Q: Evaluate the integral Jzl=2(z-1)(z+1) az. enz

A:

Q: Let X,y EIR. Prove that if 21 x +35 y = 45 then x and y are not both integes.

A: We need to prove that if 21x+35y=45 then x and y are not both integers.

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

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

Q: Evaluate the triple integral: 2 x (Iny (z) dzdydx

A: ∫12∫1x∫y2ln(y)zdzdydx=∫12∫1xz22y2ln(y)dydx=12∫12∫1xlny2-y4dydx Now,…

Q: ydzdydx x²+ y² +z? 2.

A:

Q: Evaluate the integral.

A: To evaluate: ∫221t3t2-1dt Let substitute u=t2-1 dudt=12t2-1·2tdudt=tt2-1dt=t2-1tdu Limit will also…

Q: Evaluate the integral of 3dx/(2x^2 + 4) from 0 to 0.2 * O 0.412 O 0.211 O 0.189 O 0.316

A: Evaluate definite Integral

Q: Evaluate the integral. 2/t dt 2/t dt = .2

A:

Q: R is an integral domain.

A: Note: Here we are solving problem (a) for problem (b) please submit the question again. Given: Let R…

Q: 27 Use the Fundamental Theorem of Calculus to evaluate S (Vx2 -) dx. 8.

A:

Q: Can i get help step by step with this problem?

A: Given:

Q: Evaluate the integral fff, xyzdV,where: E = {(x, y, z)|–1 <x< 1,0< ys 2,1 szs 2}

A:

Q: 3 Prove that f(x)= x² + 2x² integraliste of integrals. is on [1,1]] using definition

A: As per the question we are given a function f(x) = x3 + 2x2 And we have to prove that f(x) is…

Q: Provide a homotopic squared parameterization of side one o_1= [-1,1] x [-1,1], other than this, and…

A:

Q: Evaluate by Cauchy’s integral formula: ∫ c e3z/(z+2)4dz where c: mode z = 4.

A: To find - Evaluate by Cauchy's Integral formula : ∫Ce3zz + 24 dz where C : z = 4     Formula used -…

Q: Evaluate the integral.  integral  t  3sin 2  t dt

A: To evaluate the integral: ∫3sin2tdt. We know that, sin2x=1-cos2x2 Therefore, using this formula,…

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

A:

Q: 1. Express the integral S S f(x,y, z) dzdxdy as an iterated integral in the other five different…

A: I1=∫02∫0y3∫0y2f(x,y,z) dz dx dy0≤y≤20≤x≤y30≤z≤y2I2=∫08∫0x3∫0y2f(x,y,z) dz dy dxx=y3,y=x30≤y≤x3y=0…

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

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

Q: J (u-2) (u+3) du

A:

Q: 5, set up the appropriate iterated integrals in rios for I f dV on the indicated domains.

A: Step:-1 Given that  The equation of tetrahedron is z = 4 -2x -y⇒2x + y+z =4 ---(1) so, bounds or…