36. Integral dependent only on area Show that the value of xy? dx + (x²y + 2x) dy around any square depends only on the area of the square and not on its location in the plane.

Q: Use the Evaluation Theorem to find the exact value of the integral 10x – e" dx (Enter the…

A: We can solve the given problem fundamental theorem of calculus in order to solve the given problem.

Q: The region bounded by the curves y = x² – 3 x and y = 4 x is revolved about the line y = -4. Which…

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Q: .3 Given the integral Le-x² dx dy Sketch your 2-D region of integration on the xy-plane. Then…

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Q: Q.IA) Express integral I y + x -0,x-1 and y-0,y-1-xto T. of u- dydx in terms of (u)and (v)given…

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Q: Evaluate the triple integral. 10x dV, where E is bounded by the paraboloid x = 5y2+ 5z2 and the…

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Q: The area bounded by y=1-x²₁ x+y=1 and the x-axis is submerged vertically in the water with the water…

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Q: Compute the surface area of revolution about the x-axis over the interval [0, 1] for y = e 3x. (Use…

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Q: Find the total area between the curve y = 1- x2 and the x-axis over the interval [0, 2). Evaluate…

A: for (i) first we need to identify the region and the limits for integral to calculate the area.…

Q: Set up the definite integral for the area of the surface of revolution about the x-axis. Do not…

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Q: 5. Find the area between f (x) = cos x and g (x) = sin x for x such that -n < x < n. (YOU MAY NEED…

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Q: 6. Match the integrals with the type of coordinates which make them the easiest to do. Put the…

A: consider the first intergal ∫01∫0y21xdxdyhere, the limit of the integration is ,0 ≤ x ≤ y2   and  0…

Q: Identify u and dv for finding the integral using integration by parts. Do not integrate. 489x хе dx…

A: ∫xe489x dxBy using integration by partsu=x, v=e489x

Q: e the double integral 2(1 + x²) dA JR 1 + y

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Q: (a) Evaluate the Integrals:  ∫{2x^2 + 3}/{x(x − 1)^2}dx b) Find a horizontal line y = k that…

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Q: 1. Sketch the region of integration defined by x + y dx dy and rewrite the integral with the other…

A: Given integral is ∫y=01∫x=01-y2x+ydxdy Limits of y are y=0 to y=1, limits of x are x=0 to x=1-y2 The…

Q: Q1: By using double integrals in cartesian coordinates, find the area in the first quadrant that…

A: Area

Q: Calculate the iterated integral integral_0^2 integral_0^4 (6 x ^2y - 3 x) dy dx

A: by solving given Integral

Q: *** The definite integral representing the volume of solid generated when the area in the first…

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Q: Evaluate the line integral ſ. 8y² dx + z² dy + (100 – x²) dz over the quarter of the circle of…

A: To evaluate the below line integral. ∫c8y2dx+z2dy+100−x2dz Here c is the quarter of a circle of…

Q: 1 To find the integral x x cos 7x dx by the parts formula, use u = x and v = sin 7x, as used in the…

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Q: *** The definite integral representing the volume of solid generated when the area in the first…

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Q: b. The triple integral in Cartesian coordinates JIT »z dv that gives the value of FIRST octant…

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Q: Consider the rectangle [0,1]*[0,1), its dersity is given by plx.y)=Ke** if we Know that " (Ke** )…

A: Given: Density ρx, y=kex+y∫01∫01kex+ydxdy=ke-12……1   Dimension of rectangle is 0, 1×0, 1   To find:…

Q: owing integrals using Polar © SSx dzdy Sydydx -dydz 1+V+y -Vi-2

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Q: Evaluate the iterated integral. 4 (x + 7)dy dx Exact number, no tolerance. (x + 7)dy dx = i

A: We have definite Integration to solve.

Q: *** The definite integral representing the volume of solid generated when the area in the first…

A: Topic  =Application of integration Correct option = B

Q: The region in the first quadrant bounded by the graph of y=8-x3/2, the x-axis, and the y-axis is…

A: Given problem:- The region in the first quadrant bounded by the graph of y = 8 - x3/2 , the x-axis,…

Q: 20 Evaluate the integral dx dy by reversing the order of integration. NOTE: Enter the exact answer.…

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Q: 4. Set-up and evaluate the definite integral that represents the area of the surface generated by…

A: Formula: The area of surface generated by revolving x=f(y), a≤y≤b about x-axis is given by,…

Q: Evaluate the triple integral. 4 V16-x* V16-x²-2 ITT- S dy dz dx

A: Given integral is evaluated as follows.

Q: Evaluate the iterated integral. 8 1 (3х — 9у) dy dx - Exact number, no tolerance. 8 (Зх — 9у) dy dx…

A: Given:      ∫18∫-113x-9ydydx     =∫18∫-113x-9ydydx integrate with respect to y…

Q: Evaluate the integral by reversing the order of integration. 16 2 y3 dy dx + 1

A: Answer and explanation is given below

Q: a) Evaluate the Integrals: 2x2 + 3 x(x + 1)2 b) Find a horizontal line y = k that divides the area…

A: (a) part Consider the given integral ∫2x2+3xx+12dx Now,…

Q: 2 Sphere S to be the top half of sphere · x² + y² + 2² SS₁zdS /5 calculate the integral.

A: The given Surface is the top half of the surface x2+y2+z2=a2. To Evaluate: ∬zdS.

Q: 7. For the double integral xy² L 2xye*y dydx the region of 0s y< 1, integration D is the rectangle…

A: We use the properties of integrals and substitution to evaluate the given integral.

Q: 3. Sketch the region whose area is represented by the definite integral, and evaluate the integral…

A: Given

Q: Evaluate the iterated integral. 5 6 7 ||| ? +y² + 2) dx dy dz -5 0 0 5 6 7 | || (1²+y² +²)dx dy dz =…

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Q: plest iterate integral. 36 – x2 ,36 х dz dy dx 36 – x2°x2 + y2' dz dr de dp dφ de

A: Given that ∫-66∫-36-x236-x2∫x2+y236xdzdydx Take x2+y2=r2 Where x=rcosθ,y=rsinθ So, the integral…

Q: 4. Let h(x) = V 1+x* . Rotate the region bounded by the x-axis, y = 1+ x* for -15xs1 about the…

A: Sketching the solid generated,

Q: Set up the definite integral that gives the area of the region. Y1 = x2 – 5x Y2 = 0 dx 3 * 4 6 12,…

A: Area of the Region bounded by the curves :If f(x) and g(x) are two continuous function on a,b and…

Q: (1 – x*)² – (1 – Væ)°] dx a) Describe a solid of revolution whose volume is equal to the given…

A: Given

Q: # 4. Using the known areas, find the integrals. S,(1– |x|)dx b. S',[2 + /1– x²]dx а. -

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Q: Consider the region which lies between the line y = x-1 and the semi-parabola y =; Express the area…

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Q: 3. SET UP the definite integral that will give the area of the shaded region using a. y as variable…

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Q: Identify the variable of integration in the given definite integral. Type only one variable. ∫mn…

A: Consider the given definite integral

Q: 3. Which antiderivative of y = (1 – x²)-1 should we use to evaluate the integral (1 – x²)-' dx?

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Q: integral y cosh y dy

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Q: integrals in the order dædzdy 11 x2 1 | s(e;y, z)dydzdr

A: Please refer to the image below

Q: (2х? + у)dx + (x?у — х)dy %3D 0

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Q: Apply Green’s Theorem to evaluate the integrals ∮(3y dx + 2x dy)C: The boundary of 0≤ x ≤π, 0 ≤ y ≤…

A: According to Green's theorem - ∮Pdx+Qdy = ∬D dQdx-dPdydxdy          ...............(1)Given integral…