Use Simpson's 13 rule (1) and the Trapezoidal rule (2) to numerically integrate the following function with a4. Find I A-? a) 1,13 b) 1,26 )134 d) 1,38 1,42 Boş birak

Q: f(x, y, z) =(x²+y²+z) 2

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Q: Use spherical coordinates to evaluate the triple integral x² + y² + z² dV, where E is the ball: x² +…

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Q: 2. If f e R[a, b], show using the properties of Riemann Integrability that there exists M > 0 such…

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Q: 4. Evaluate the integral f. x'y°dy – x°y'dx, where C is the square determined by the lines x = 0, y…

A: As per Bartleby's answering policy, we can answer only one question and here we have answered the…

Q: A muliple regresion of y on a cnstant x and x produces the folloing resuls. j= 4 +0.Ax + 0.9%, R =…

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Q: Use Green's Theorem to find the work done by F(x,y)=x(3x+y)i+xy^2j in moving a particle from the…

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Q: Find the sum of maximum and minimum values of the function f(x, y, z) = 9x + 18y + 27z on the elipse…

A: Using Lagrange Multipliers with Two Constraints to find the maximum and minimum values of the given…

Q: Let C:z|=1 in the counterclockwise direction and I = $. dz, J = f. Lnzdz, and K = $. tanzdz. For…

A: We can apply cauchy Goursat theorem on I and K but not on J

Q: Find the sum of maximum and minimum values of the function f(x, y, z) = 6x + 12y+ 18z on the elipse…

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Q: Find the maximum value of f(x, y) = 9xy(5 – 25x – 5y) over the triangle with vertices (0,0), (, 0)…

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Q: 12. Consider the lamina covering the regon x442-2,0EXET WH aunsity functionplx,u) = - 5x + 2u+5. 1ts…

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Q: AXYZ is isosceles with base YZ and M is any point on YZ. Prove that a. ZXMY > ZY Z. b. XM < XY M

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Q: Evaluate the triple integral ///. zdV, where E 4. is bounded by the cylinder y2 + z? = 4 and the…

A: According to the given information, it is required to evaluate the triple integral.

Q: |s, is calculated by the thorem of divergence of the full range straight flux F(x, y, z) = 2xỉ + yj…

A: Answer  Flux = 2π

Q: Use Gauss Divergence theorem to calculate (5zi+ 4yj- 2z k).n dA over the sphere S: 2 + y? + 22 = 9.

A: This is a problem related to vector calculus. Based on the general formula of gauss divergence…

Q: Evaluate the following. dV where R is the portion of the ball of radius 1 in 4-dimensions with all…

A: We need to evaluate the value of integral in 4 dimensions.

Q: Find the maximum value of f(x, y) = 3xy(9 – 45x – 9y) over the triangle with vertices (0,0), (5, 0)…

A: Given that fx,y=3xy9-45x-9yfx,y=27xy-135x2y-27xy2 Now, let fx=0 &amp; fy=0…

Q: Solve the integral. + yz )do; o: part of the plane x + y +== 6 that lies in the first octanct.

A: Solution:

Q: 1. Evaluate the integral: SSf, xe**+y<+zt dV where B is the portion of the unit ball x² + y² + z² <…

A: Here, the region B is the portion of the unit ball x2+y2+z2≤1 that lies in the first octant.…

Q: Evaluate the triple integral. 10x dV, where E is bounded by the paraboloid x = 5y? + 5z2 and the…

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Q: Evaluate both sides of divergence theorem for A = pa, + pcos()a,+ za, through the closed surface…

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Q: Use either form of Green's Theorem to evaluate the following line integral. $9x²1² 6 C $9x³y² dx +…

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Q: - Prove that the contour integral – z)dz = -12i where C is the triangle with points 0, 3i and -4…

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Q: FD is the region in the first octant between the spheres x2+y2+z²=1 and x2+y2+z²=16, then dV =

A: Converting into spherical coordinates

Q: The area of the region under the curve A(x) = 2x+e between 0.5sxs2.0 with h 0.25 is estimated by the…

A: We have to use rectangular method to find area of the function A(x) = 2x+ex. Let's understand the…

Q: The equation dy + v y² + ¢y+x = 0, dt where y, 4, and x are functions of t, is called the gen-…

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Q: Evaluate fz² In z dz using integration by parts O² Inz-+c Onz-+c Onz-+c 2²lnz - 2 + c 12 21

A: Solution:  step-1: Evaluate ∫z2*lnz dz using integration by parts                Formula for…

Q: Evaluate both sides of divergence theorem for A= pa,+ pcos()a+ za, through the closed surface…

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Q: Calculate the trapezoid approximation of 5dx using four subintervals. O T5 = 0.60 O T5 = 0.40 O T5 =…

A: The trapezoid approximation of the given integral is given below.

Q: 4. (a) Use the trapezoidal rule to numerically integrate from a = 0 to b= 2 /(z)-0.2+25 +3r

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Q: Evaluate both sides of divergence theorem for A = pa, + pcos(ø)a, + za, through the closed surface…

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Q: . Set up the triple integral fSSp r+y+zdV, where D is the tetrahedron with vertices at (0,0,0),…

A: The equation of tetrahedron with intercepts (a,0,0), (0,b,0) and (0,0,c) is given by: Given…

Q: Evaluate the triple integral. 4x dV, where E is bounded by the paraboloid x = 7y2 + 7z² and the…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Evaluate the triple integral ryz dV, where T is the solid “tetrahedron" with vertices (0,0,0), (0,…

A: Identify the limits of integration from the region. The base of the tetrahedron is in the xy-plane.…

Q: Evaluate both sides of divergence theorem for A = pa,+ pcos(ø)a,+ zaz through the closed surface…

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Q: 7. Use Green's Theorem to compute the line integral | ry? dx – x² dy, where C is the triangle with…

A: ∫xy2dx - x2dy triangle vertices are (0,0), (2,0), and (2,2)

Q: evaluate both sides of divergence theorem for A= ra,+rcos(8)a , +r²a, through the closed surface…

A: Given problem is :

Q: The measurements x1 = 10m, x2 = 8m, and x3 = 6m represent the sides of a rectangular parallelepiped…

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Q: .The primal form of SVR with soft margin is M 1 min |w+CE(6i + &;) i=1 s.t. y) – w"x1) – b < e+ §i,…

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Q: #1. Evaluate (2x – 5y) dA, R where R is the parallelogram with vertices (0,0), (2,3), (–1,4) and…

A: The given region R is a parallelogram with vertices as shown in below graph. We have to use change…

Q: Let S be the sphere of radius 2, oriented inward. Let F = (2x + e", 4y + e*, 2:2). Use the…

A: In the given question we have to solve the double integral s.t∫∫F.ds  to the help of divergence…

Q: In his work Nova stereometria doliorum vinariorum (New Solid Geometry of a Wine Barrel), published…

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Q: $ ((x,y) (E,6) )e product Prove 2 xt + 3yt on e?. Gompute inner IL(,2), where the norm i's…

A: We have to prove that f( (x, y) , (t, t) ) = 2xt + 3yt is an inner product on R2 . 1.) &lt; ( 0, 0 )…

Q: Use Green's Theorem to evaluate S. axy dy + cxy dy, where C is a counterclockwise oriented…

A: Given : a=2, c=8 We have to use Green's Theorem to evaluate            ∫C axy dy+cxy dy where C is a…

Q: Evaluate the triple integral. 8x dV, where E is bounded by the paraboloid x = 7y2 + 7z2 and the…

A: here, E is bounded by the paraboloid  x=7y2+7z2  and the plane x=7.    so , at    x=7 ,     y2+ z2…

Q: Evaluate / (7xi – zk) · ndA over the sphere S : x² + y² + z² = | S a) by divergence theorem, (b)…

A: a) By divergence theorem, ∬SA. ndA=∫∫∫V∇.A dV Now,  ∇.A=∂7x∂x+∂0∂y+∂-z∂z=7-1=6 By changing to…

Q: Evaluate both sides of divergence theorem for A= pa, + pcos(0)a , + zaz through the closed surface…

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Q: Find a parametrization of the curve x^(2/3)+y^(2/3)=8^(2/3) and use it to compute the area of the…

A: Finding the parameters:

Q: Use Green's Theorem to Calculate the Line Integral ſy²dx + x²dy, where c is the triangle o vertices…

A: Given that, the line integral is ∫y2dx+x2dy and the vertices of the triangle is 0,0,4,0 and 4,4. By…