d) Use line integral method to evaluate JR F(x,y)•dr where F(x, y) = (3x²y³ï+ 4xy²j) and M , N,K are the last three digits of your index number which is M+N+K (0,2,8) and R is bounded by the curvesy = x² and y = x %3D

Q: Express integral I y + x (-4x-2y) -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: S, (3x² – 3yz + 2xz)dx + (3y² – 3xz + z²)dy + (3z² – 3xy + x² + 2yz)dz Calculate the curvilinear…

A: Let's find.

Q: 2y Calculate the double integral in a general region where z = x² +1 0, x= 1, y = 0, y = √√x bounded…

A: Since you have posted multiple questions, we will solve the first question for you. If you want any…

Q: 1. Evaluate the triple integral over the indicated bounded region E JII y dv, - {(z, y, 2) | 0 < = <…

A: It is problem of triple integration

Q: b) Use double integral to find the area of the region that is bounded by the lines y = x - 2 and y =…

A: Double integral is used to integrate the function of two variable over two-dimensional region.…

Q: Use Green's Theorem to evaluate the line integral a-x)dx + (2x - x) d for the given path. C:…

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Q: 3. Sketch the region and evaluate the iteraterd integral (a²y – ry?)dydx. 2.0 1.5+ 1.0 0.5 0.0 0.0…

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Q: Plot a direction field and some integral curves for xy' - 2y = -1 (A) on the rectangular region {-1…

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Q: 16. By inspection, a simply-connected and continuous region R A. has no holes and is closed. B. has…

A: Introduction: The application of connected regions is very significant in different fields of…

Q: Use Green's theorem to find the line integral of 2x dx – 7x2 dy counterclockwise around the triangle…

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Q: 3 Find the abscissa of the centroid of the region between the parabola y = 9 − x2 and the line y…

A: Given :The parabola y=9-x2 and the line y=2-2x from x=0 to x=2.To find :The abscissa of the centroid…

Q: If F = (x², x²) and C is the boundary of the region $o FT ds by using Green's Theorem. (i.e. use a…

A: Given, F=&lt;x2,x2&gt; And the region C is bounded by y=x2 and y=x.

Q: y + x -0,x-1 and y=0,y-1-xto T.of u- dydx in terms of (u)and (v) given that: Region bounded R: x…

A: Evaluate, ∬Ry+x-4x-2y2-412dydx                        …1 Region R: x=0, x=1 and y=0, y=1-x u=2y+2x2…

Q: Sketch the region R bounded below by the curve y = x², on the left by the line x = 1 and above by…

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Q: Find the centroid of the region bounded by the graphs of y = x + cos x and y = 0 for 0&lt;=x&lt;=…

A: Graph is given below:

Q: Let R be the region bounded by the parabola y = x 2 − 1 and the line y = x+ 1 and let f(x, y) = xy…

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Q: 2. Find the area of the region bounded by y = e*, x = 0, x = 2, y = 0 using definite integral %3D…

A: This is a problem related to integration application. Based on general formula we will solve the…

Q: 5. Set up an iterated triple integral in the order dxdzdy that gives the volume of the solid in the…

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Q: Set up a double integral that gives the area of the surface of the graph of f over the region R.…

A: To find the area of surface of graph f

Q: 3) Show that the line integral is independent of path and then evaluate the inte S, sin y dx + (x…

A:

Q: Calculate the double integral in a general region where z = 2y bounded by x = x²+1 0, x= 1, y = 0, y…

A:

Q: Consider calculating the size of the region N:= {(x, y) E R² : y > v3x², æ² + y² < 4} , with the 2d…

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Q: Consider the region bounded by the graphs of y: 2e* – 1, y = e*, and y = 2 shown in FIGURE 6.2.12.…

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Q: Find the limits of integration for double integral [[ f(x,y)dxdy over the given D region of…

A: Introduction: When a double integral is described within a region enclosed by a circle, we can…

Q: Set up an iterated double integral equal to the line integral P (y + ev") dx + (2x + cos y²) dy…

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Q: Sketch the region R whose area is given by the iterated integral. dx dy 21 1.5 1.5 y 1- y 11 0.5…

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Q: compute the line integral of the function f(x,y,z) = x^2 +3y along the circle x^2 +y^2=4 from (0,0)…

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Q: Sketch the region R whose area is given by the iterated integral. 8 (64 - y2 dx dy 60 8. 50- 6- y 4…

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Q: Compute the line integral of the function f(x, y, z) = x^2 + 5y along the circle x^2 + y^2 = 4 from…

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Q: Find the centroid of the region bounded by the given curves. y = 8 sin(4x), y = 8 cos(4x), x = 0, TT…

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Q: Determine the ordinate of the centroid of the area bounded by the curve x^2 =8y and the line 2x-y=0

A: Given curves are x2=8y and 2x−y=0. We have to find the ordinate of the centroid of the area bounded…

Q: Find the centroid of the region bounded by the given curves. y = 6 sin(5x), y = 6 cos(5x), x = 0, X…

A: In the question we have to find centroid of the region.

Q: 2. Find the centroid of the region bounded by the parabola y=x² and the line y=4.

A:

Q: Use Green's Theorem to evaluate the line integral S (y-x) dx + (2x - y) dy for the given path. X C:…

A: Green's theorem: ∫CMdx+Ndy=∫∫R∂N∂x-∂M∂ydA   Given: I=∫Cy-xdx+2x-ydy and C: y=x and y=x2-2x It means…

Q: Compute the surface area of revolution of f (x) (x + 1)z about the x-axis over 3 [0,1]

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Q: Calculate line integral F-dr where F(x, y) = (7x + y, 5x + 2y) and C is a rectangle with vertices 0,…

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Q: 2. Sketch the region of integration of the given integral Q in #1. Set up Q by reversing its order…

A: The integral is given as Q=∫01∫y2yx-ydx dy. We need to sketch the region of integration of the…

Q: Use Green's Theorem to evaluate the line integral Jo for the given path. C: boundary of the region…

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Q: 2. Find the value of the line integral foF dr without using Green's Theorem, where F(x, y) = (x+y)i…

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Q: 2. Find the coordinates of the centroid of the the region bounded by f(x) = x – x² from x = 0 to x =…

A: Question 2Here we have to find the centroid of the region bounded by f(x)=x-x2; x = 0; x = 1.First…

Q: Find the abscissa of the centroid of the region between the parabola y = 9 − x^2 and the line y = 1…

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Q: = Compute the area of the region bounded by y hyperbolic or inverse hyperbolic functions. 1 √x²+16…

A: We compute the area of the region bounded by y=1/√(x2+16) over the interval [ 0,3 ] hyperbolic or…

Q: Calculate fc F dr where F ( x, y) = (x 2+ y, 3x - y 2) and C is the positively oriented boundary…

A: We have to calculate ∫C F · dr, where F(x, y) = 〈x2 + y, 3x − y2〉 and C is the positively oriented…

Q: Sketch the region R bounded below by the curve y = x², on the left by the line x = 1 and above by…

A: The region bounded by the curves is as below:

Q: 2. Determine the centroid of the area bounded by the curves y = 4x + 16, x = -2, x = 5 and x-axis.

A:

Q: d) Use line integral method to evaluate F(x, y)• dř ,where R 1 F(x, y) = (3x y°i + 4xy² j) and M, N,…

A: The graph of curves y=x2, y=x is as follows The yellow colored region is region R

Q: Evaluate the lino integral y+ + (4+2-x>y +2が Where C consitts of line segments from 0,-,2) to…

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Q: 8) consider the region R in the first quadrant(xz0, y2) bounded by x=2y² X=Y²+1 a) set up, but clo…

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Q: 4/ Find the area of the region enclosed between the curves y= cos 2x , y=0, x=TT/4, x= TT/2 ? ans/…

A: Given-y=cos(2x)y=0x=π4x=π2Let consider that area of the curve is =AWe have two value of x and two…

Q: Evaluate the integral (y-x)drdy over the region D in the ry-plane bounded by the straight 1 lines y…

A: We have to find the value of the double integral over the region bounded by the given lines. It is…