Q7 For which of the following values of m is the area of the region bounded by y = x - x² and y = mx equals a) 4 b) 2 c) -2 d) -4

Q: If R is the region such that / ev* dA eu" dæx dy, then the area of the region R is: O a. 24 O b. 4 O…

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Q: By making an appropriate change of variables, evaluate the double integral (z + y)e* v*dzdy R. where…

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Q: Evaluate the integral SR 8xydA, where R is the triangle 8x + y 0, y 2 0. SR 8zy dA =

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Q: Assume that D is bounded by the lines y = x +1, y = x, x = 0, and æ = 1. Calculate: S Sp e22 dA =…

A: Given : y=x , y=x+1 x=0, x=1 To find integration of e²² da

Q: 1. Evaluate each iterated integral. (a) x dA over the region R bounded by x? + y? = 36, y = v3x, and…

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Q: Below is the solid Q bounded by the surfaces S,: x? +y? +z? = 4, S;: z = V3 and S,: y= x in the…

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Q: If R is a region bounded by y = x² and y = 4x – x², evaluate S. | (x + y)dA R

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Q: Consider the surface S: z = 4 - x2 ,bounded by y = −5(x2 - 1) and y = 0, just as it is shown in the…

A: We have to find the area of the surface S, and we will use surface integral to do that.

Q: Let D be the region in R2 bounded between the parabolas y = 2x² and y = 1+x², Which of the following…

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Q: Use Green's Theorem to evaluate n ds, where F = (Va + 5y, 4x + 5y) and C is the boundary of the…

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Q: Let D be the closed region in R? bounded by x2 - 2xy + y² + x + y = 0 and Q3. x + y + 2 = 0, as…

A: Given: x2−2xy+y2+x+y=0x+y+2=0

Q: *** Which of the following represents the area of the region bounded by y= x+2 and y= x² ? 2 „x+2 SL…

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Q: Which of the following represents the area of region B? O9 (2) - f(2) dz Sa f (x) da So f (z) da Off…

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Q: H.W Ennlunte where o is the selid bounded by the Sur faces xサ 0 7 そー

A: Given term is: ∫∫∫Sx2+y2dzdydx and the surfaces are x2+y2=z2, z=0,z=1

Q: If R is the region enclosed by x-axis, y = -3x and x = -2, then evaluate the following double…

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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: 2. Evaluate S SR 72xydA by making appropriate change of variables, where R is the region bounded by…

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Q: Given the region D in the first quadrant enclosed by x = 0, x = y², and y = 2. Express D as a region…

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Q: Evaluate by two methods the integral || ydA, where D is the region bounded by the line r - y = 0 and…

A: compare two equations (x,y) = (-1,-1) (x,y) = (2,2) from second parabola equation x = -2  then y = 0…

Q: Use symmetry to evaluate the given integral. (7 Зх + 2y) dA, - where D is the region bounded by the…

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Q: 3. Use the substititutions u = y – x, and v = y +2x to evaluate the integral (2x +y)(x – y) dx dy…

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Q: If F = xy?i + yz? j + zx2k, and S is the region bounded by the triangle with vertices (1,0,0),…

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Q: By making an appropriate change of variables, evaluate the double integral = || (x + y)e²-y° dædy R…

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Q: Calculate the middle rectangle approximation of , Vxdx using five subintervals. O M5 = 0.624 M5 =…

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Q: If the region R is bounded between two circles x² + y? = 1, x + = 4, then we have: ev+ dr do dA = +…

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Q: Evaluate the integral o f(z) dz, where C is the unit circle enclosing the ori- C gin, and f(z) = zz.

A: Given-A circle C,which is unit circle enclosing the origin           -f(z)=zz  To find- ∮Cf(z)dz

Q: If D is the region enclosed by y = 1, x = 7, and y = 7x. Then Select one: True O False Jy dA = 693.…

A: The region D is enclosed by  y=7x,x=7,y=7xto find the value of  ∫∫D14ydA

Q: 7. Let E be the region in R enclosed by the cone z = Va2 + y? and the paraboloid z = a2 + y?. Then…

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Q: Let E be the region in R³ bounded by the surfaces x² + y² = a², z = 0, and z = h. What does the…

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Q: Find the value(s) of c such that the area of the region bounded by the parabolae y = x² – c² and y =…

A: Topic = Application of integration

Q: Evaluate the given integral Q. Q = ff (√5 - x) dA, R where R is the region bounded by y = x and x =…

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Q: Evaluate the integrul )}EA where f(x,y)=In(x*ッ) is the by the circles x?+y?=9 and the and D cegion…

A: Given information: The function is f(x,y)=lnx2+y2x2+y2 and the region of the integration is x2+y2=9,…

Q: 1 ydx 2 5 (wdy – ydr). P = xdy - C C

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Q: If D is the region enclosed by y = , x = -3, and y= 0, then: II.-96y° dA =1. Select one: O True O…

A: Given problem:-

Q: Evaluate the following integral. 9. y) dA, R is the region bounded by y%3D and y = 5-x 4x R.

A: Given : y=9/4x, y=5-x

Q: 2. Find the value of the integral of g(z) around the circle |z- il = 2 in the positive sense when 1…

A: Cauchy integral formulae: Let us define function f: D→ℂ and a∈D and 'C' is any closed curve around…

Q: The value of the double integral // (2x²y + 9y') d A, D where D is the region bounded by x and y = 2…

A: Given problem:-

Q: /| f(r,y) dA = f(r, y) drdy + /. II F(7,y) dzdy

A: Solution:

Q: : Evaluate ff,(x + 2y)dA, where D is the region in space bounded by y 2x and y = 1+ x2.

A: The given region D is bounded by the curvesy=2x2 and y=1+x2.We will find first the point of…

Q: Use Green's Theorem to evaluate rids, C where F = (Va + 6y, 3x + 6y) C is the boundary of the region…

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Q: compute the area of ∫ D∫4xy-y3dA when D is the region bounded by y = √x and y=x3

A: Given  The given integral is ∫D∫4xy-y3dA. Region bounded by y=x and y=x3. Apply formula…

Q: The net of a cone consists of three different two-dimensional areas. O True O False

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Q: Evaluate the following triple integral Vr² + y² + z²dV where V is the space region bounded by a? +…

A: Cartesian co-ordinate and spherical co-ordinate x=rsinφcosθy=rsinϕsinθ z=rcosφx2+y2+z2=r2

Q: 5. Evaluate the integral fffn 7 dzdydr, where R is the region enclosed by ² + y? 2 = Zz²+y² .

A: To convert the cartesian plane into cylindrical coordinates, Put and

Q: Evaluate drdy over the region R which is enclosed by the lines r+ y = ±1 r + y + 2, and r – y = ±1

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Q: Using Green's Theorem, calculate the area of the region bounded above by y = 5x and below by y =…

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Q: ral by making an appropriate change of variabl re R is the region enclosed by the lines y = 6x

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Q: Use the Cauchy integral formulas to evaluate the eiz cos z dz, Yo z2(2z – 37) | where C is the…

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Q: he region bounded by the cylinder x2 + y2 = 9 and the planes z=0 and x +z =9 O 243 O 81T 27TT 729TT

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