C'alculate | (ydæ – xdy)] wherein y(t) (2cos(t), 2sin(t)), 0 < t < 27, is an circumference that delimits the set K = {(x, y) E R²; a² + y? < 4}

Q: Suppose at x = x, Vf(x) = 0. What can you say about x if (a) f(x) is convex? (b) f(x) is concave?…

A: In multivariable calculus ∇f is similar to df/dx of single variable calculus &amp; the ∇²f is…

Q: Consider the right triangle withvertices (0, 0), (0, b), and (a, 0), where a &gt; 0 and b &gt; 0.…

A: Given right angle triangle has vertices  (0, 0), (0, b), and (a, 0), where a &gt; 0 and b &gt; 0.…

Q: Evaluate the line integral 2 Cx2y)dx- 2xdy along each of the following closed paths, taken…

A: Given that the integral,

Q: 2. Evaluate f (3x + 4y2) dA, where R is the region in the upper half-plane 15 bounded by the circles…

A:

Q: The absolute minimum of f (x, y) = x² +y² – 2y on the semicircle region D= {(r,y) | y> 0, x² + y? <…

A: Given function is fx,y=x2+y2−2y and D=x,y|y≥0,x2+y2≤4. We have to find the absolute minimum of fx,y…

Q: -JIL e √x² + y² dv, where E is the region that lies inside the cylinder x² + y² = 4 and between the…

A:

Q: c) x+2y) dA, where D is bounded by the parabolas y=2x2 and y =1+x?.

A: C) The area D bounded by the parabolas y=2x2 &amp; y=1+x2 is as shown below. The red graph is of…

Q: Let D be the half-disc in the xy-plane given by x +y <9. Calculate e-(x2+v)dA

A:

Q: dr Consider the integral I- composite Trapezoidal rule with n-4 subintervals is: The approximation…

A:

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

A: Maximum value occurs at critical points or on the boundaries of the triangle.

Q: 3. Find the area of the band cut from the paraboloid x² + y² -z = 0 by the planes z = 2 and z = 6.…

A:

Q: |Use Green's Theorem to evaluate | -x'ydx+xy°dy where C is the boundary of the C circle x + y =16…

A:

Q: Calculate the trapezoid approximation of o xdx using four subintervals. O T5 = 21.52 O T5 - 23.25 T5…

A:

Q: Compute 3xy dS, where S is the surface of the tetrahedron with sides z = 0, y = 0, x + z = 1, and x…

A:

Q: Show that T(u, v) = (u² – v², 2uv) maps the triangle = {(u, v) : 0 < v < u < 5} to the domain D…

A:

Q: Verify Green's theorem for Q7 [x(x? + y²)dx – y(3x² – y²)]dy Where C is the boundary of the triangle…

A:

Q: soùd lines For Portions dash ùnes of borndry included in thee bmain and not include Suot1 For d)…

A: We are asked to find the domain of the function.

Q: re 2" dr + (x* + 2a²y?)dy where C is the boundary of the region between the circles a² + y? = 1 and…

A:

Q: c) By using Green's theorem, evaluate (In (r) + ry – y²) dx + (e" +x²y - 3ry) dy, where C is the…

A: Green's therorem establishes relationship between double integral and line integral. Double integral…

Q: Verify Stoke's for F = (2x – y)i – yz²j – y²zk where S is the upper half of the sphere x? + y? +z² =…

A: Solution is given below

Q: O By using Green's theorem, evaluate $ (In (2²) + æy² – y²) dæ + (ev + x²y – 3ry) dy, where C is the…

A:

Q: 3. Find the area of the band cut from the paraboloid x² + y? – z = 0 by the planes z = 2 and z = 6.…

A: Let's find.

Q: Evaluate ||| Vx2 + y2 dV, where E is the region that lies inside the cylinder x2 + y? = 25 and…

A:

Q: (a) Compute the area of the portion of the cone x2 + y2 = z? with z 2 0 that is inside the sphere x2…

A:

Q: Find b∈R such that ∫∫Ssin (b) ydS = 8, where S is the part of y^2 + z^2 = 4 that is between x = 0…

A: To find the value of b satisfying the given integral.

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

A:

Q: For the qutegradsSEddy tringle Over the bounded by -0,4=0 and *+y=l-

A: We have to find the integral  ∬e2x+3y dx dy   over the region R bounded by curves: x=0, y=0, x+y=1

Q: Given the figure: 23)The area of R2 using vertical strip is given by A. -xkx А. С. R1 В. (x-x kdx D.…

A: As per the guidelines,we are suppose to answer only one question ( out of 27 and 28 question)…

Q: 10. Using Stoke's theorem, evaluate y dx+ xz dy+x² dz where C is the boundary of the triangle cut…

A:

Q: consider the curue desoribed by 2y"-x²_4y vevity that the foint (4-25 les on this o8 wrE andd find…

A:

Q: The area enclosed between the curves p(a) =2 +*+ 3 and g(@) = -22 - * + is O 16 47 %3D 18 49 O -49…

A:

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: 3. Evaluate the integral *zp- where C is the circle |2| = 2.

A:

Q: Let X - Y (3, 0.02). Given Ttx = 300 calculated by the Esscher Premium Principl %3D

A: From the given information, X~γ3, 0.02 fx=0.023γ3e-0.02xx3-1, x&gt;0       =0.000004e-0.02xx2,…

Q: Find the line integral (4х — 5у) ds, where C is the semicircle y = 9 – x² traversed from (3,0) to…

A: Graph the semi-circle. Take x=3cost and y=3sint Now, x'=-3sint and y'=3cost The angle covered by…

Q: 56 Consider points P and Q in the x-y plane, with P = (1,0) and Q = (0,1). The line integral %3D Q…

A: Line integrals

Q: Evaluate [[[ =*dxcydz over the sphere x +y² +=² =1.

A: to find:- to evaluate the given integral.

Q: Evaluate ||| Vx² + y² + ²²&V where S lies above the cone z = Vx² +y° and between the spheres x + y…

A:

Q: (2,2) b) Evaluate o x*y dx + x dy, shown in adjacent figure using green's theorem. where c is…

A:

Q: Let W = Span{u} where u -2. Let y = |1, find the distance from y to W L3]

A:

Q: d). Integrate f(x, y, z) = -√√x² + z² over the circle r(t) = (a cost)j + (asint)k, 0≤t≤2.…

A: Solution:-

Q: B is the first quadrant part of the region enclosed by the circles x2 + y? = a? and x2 + y? = b2…

A:

Q: two x' dA, where R isa Regian bounded by fufcirck xye 1- x"rye-a' and x ty?=b² 2 SS(x*yj*dA, whera R…

A: Note that this is a multipart question, so as per the company policy, we can solve only the first…

Q: . SS, xcos(y)dA, D is bounded by y = 0,y = x² ,x = 1.

A: See the details solution in below

Q: se the Divergence Theorem to evaluate (8x + 12y + z2) ds Is here S is the sphere x2 + y2 + z² = 1.

A: To compute the below integral using divergence theorem.

Q: Evaluate dV, where E lines between the spheres a+ y + z = 9 and E 2 + y2 + z? x2 + y? + z2 = 16 in…

A: The answer is in step 2

Q: 35. Above the cone z = a² + j? and below the sphere x² + y² + z² = 1

A:

Q: 7. Find the area of the portion of the plane z = 2 y that lies directly above the circle x+(y-1) =1…

A:

Q: Solve the fAllowing equetiun by cepuration of warnoble methal xQu-y Du t Zy = X Y glven uli,1)= 3…

A: