The region R shown in picture is bounded by x +y =1 and x -axis. Set uj [[f(x,y)dAas: R

Q: Find div F for F(x. y, 2) = (xy, 5 - zy, x +y). Select the correct answer below: O x- O y-? O x-5- O…

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Q: Let F = (y – x, ry) and let C be the line segment from (2, –3) to (1, –1). %3D Evaluate F. dr.

A: We wil first equation of parametric equation of line segment

Q: A fair coin is tossed two times independently. Let H₁ = {1₁ (1, if head is obtained at the ith toss…

A: When head is obtained at 1st toss then H1= 1  When head is not obtained at 1st toss then  H1= 0 When…

Q: Find 4rye®y? dA, where R [0, 1] × [0, 2]. R

A: The objective is to find the double integration where  R=[0,1]×[0,2]

Q: 2. For F = (xz3, 2y*x²,5z?y) find: a. div F b. Curl F and find div(curl F) C.

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Q: The area bounded by the curve y3a and the lines z 4 and a-9 above the z-azis is aquare units O 27v0…

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Q: Find the adjoint of F:C3 tends to C3 defined by F(z1, z2, z3)=(2z1+(1-i)z2 , (3+2i)z1 -4iz3 ,…

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Q: Evaluate F.dr where F(x, v)=xyi (4, 0).

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Q: For which values of ß does {(1,0, ß),(1,2,–3)(B,1,0)} span R'?

A: If spans the same subset of R³, the vectors must be linearly dependent to each other.    Therefore,…

Q: Let F(x, y, z) = (14xyz + 7sin(x))i + 7x²zj + 7x²yk. Find a function f such that F = Vf. f(x, y, z)…

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Q: H.W: Find fr, fyand f if f(x,y, z) = x-Vy +z

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Q: 2 Find f, fyand f. if f(x, y, z) = x-Vy + z°

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Q: Let C1 be the line segment from (1,0,1) to (0,3,6). Evaluate dx + dy + dz.

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Q: Calculate the rectangular approximations R1, R2, and R4 for f(x)=2x−1 over the interval [1,5].

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Q: || x dA, R is bounded by y = x, 2x + y = 6 and the y-axis. R

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Q: Find // VdA, + 1 R -dA, R= [0,3] × [−1,1]

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Q: Find f, and f, for f(x,y)=y In (3x +4y). fx fy

A: When the partial differentiation is done with respect to a specific variable, then all other…

Q: (4xy) w = 3 sin (4xy tan (z) +4 In (5yz)- 8 e

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Q: Evaluate [², dx V4-x2 2.

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Q: 6. Simplify the following. Show all details and leave your answer with only one trig function, no…

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Q: Let F = (2xz+y², 2xy, x²+1), if Vf= F, find f(1, 1, 1) – f(0, 0, 0)

A: Given vector funtion and

Q: be the vector spaces consisting of zero and polynomials in z of degree <3 and degree < 6…

A: Given that  and  are two vector spaces consisting of  and polynomials of degree  and degree…

Q: (f) Construct a model to predict maximum temperature of the battery during discharge (in K) as…

A: It is wanted to be investigated by the researcher whether or not the energy capacity in watt-hours…

Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.