Evaluate the double integral S, x dx dy where the region R is bounded by: 9 y = 4x – 3, 1 +x. 4 у %3 4x — 18, у 1 x + 4 y 2 4

Q: Evaluate the triple integral (x + y) dV over the bounded region E E = {(x, y, z)|0 < x< y – 1, 0 < y…

A: Given data:   The given triple integral is ∫∫E∫x+ydV. The limits of x are [a,b]=[0, y-1]. The limits…

Q: Graph the region of integration and evaluate the integral S, (→+x² ) dA {(x,y)|1<x² +y² < 4 and 0 <…

A: • The region R has circular symmetry, so we will use polar coordinates to evaluate this double…

Q: Evaluate the double integral where D is the region bounded by y = x and y = 2\x. || (2yx2 + 9y³) dA

A:

Q: Evaluate the triple integral over the bounded region E = {(x, y, z)la s xs b, h,(x) sysho(x), e s zs…

A: Given: ∫∫∫E2x+5y+7z dV

Q: Evaluate ffysin(xy)dxdy น over the region bounded by xy = 1, xy = 4, y = 1, and y = 4 using x == , y…

A: We have to find the area using double integration.

Q: Evaluate the integral ∬R(x−y2)dxdy over the region R= {(x,y)|2≤x≤3, 1≤y≤2}.

A: Given integral is where

Q: SSR e-x² dxdy

A:

Q: B: Represent the region shown in figure (2) by double integrals of order dydx, dxdy and rdrde. y =…

A:

Q: 5xcos(y)dA, D is bounded by y=0, y=x2 ,x=9

A:

Q: Consider the double integral //(y - x) dæ dy I = R where the finite region R is bounded by the lines…

A:

Q: Evaluate fSR f(x, y) dx dy, where R is the region given by 0<x < 2;0 < y < 5 and f(x, y) = 1 – ² –…

A:

Q: 1 -drdydz JSJ (x² + y² + 22)#

A: Use spherical coordinate system to solve it.

Q: Evaluate the double integral + y? )dædy, where N is a bounded region between y = x² and y = x³.

A:

Q: Find double integral over the rectangular region R with the given boundaries.

A: ∬x+ydydx; 1≤x≤3, 0≤y≤1

Q: Evaluate the double integral // f(x, y)dA over the region D. f(x, y) = 3, D = {(x, y)|0 < x < 1, ² <…

A:

Q: Integrate f(x, y) = x over the region D bounded by y = x and y = 6x + 7. x dA

A:

Q: Evaluate the integral. SSS_* √x² + z² av E where E is the region of integration bounded by the…

A: To solve this put x=rcos(theta) And z=rsin(theta)

Q: Evaluate the double integral for the function f(x, y) and the given region R. f(x, y) = 3y + 3x; R…

A: To find- double integral of the given function.

Q: Use the region R with the indicated boundaries to evaluate double integral.

A: Use the Fubini's theorem, ∬f(x,y)dA=∫ab∫cdf(x,y)dydx and write the double integral, ∬x2y2dxdy as…

Q: s) Evaluate the triple integral, 1– y – 2) dV where E is the region given by E = {0SES y, 0<y< 4,…

A: Solution

Q: Compute the integral ∫∫D xy dA where D is the region bounded by y = √x, y = 6−x, y = 1.

A: Consider the given function, y=x,y=6-x and y=1 Put both the function equal to find the limit.

Q: 1. Evaluate the integral JS aA, where R is the region: {(x,y)|0 < x < 1, –3 < y< 3] x²+1

A: To evaluate the integral: ∫∫Rxy2x2+1dA where R is the region (x,y)|0≤x≤1,-3≤y≤3.

Q: 2. Evaluate the double integral STR (x+ y) dA over the region R give by R= {(x, y) : y > x², y <…

A:

Q: 5. Show that, in the region bounded by y = Vx and y = x2 the following double integral 3 (х + у) dA…

A:

Q: Suppose that f(x, y) = x + 6y and the region D is given by {(x, y)| – 3 < x < 3, – 3 < y < 3}. - D…

A:

Q: y = Vx (1,1) jdy y = x (0,0) Suppose that the double integral: SLLis(x, y) dxdy B as bounds defined…

A: From the given region: We can write as: I=∫y=xy=x∫x=0x=1fx,ydxdy Therefore, A=0B=1C=xD=x Now solve…

Q: Evaluate the integral ∬Rcos(x+y)dxdy over the region R= {(x,y)|0≤x≤π4, 0≤y≤π4}.

A: Given:

Q: Sketch the region R whose area is given by the iterated integral. * 64 – y² dx dy 60- 50- 40- 30- 20…

A:

Q: Calculate the double integral S TR (2x + 8y + 16) dA where R is the region: 0 < x < 4,0 < y < 1.

A: we have to find the double integral  ∫∫R(2x+8y+16)dAwhere R is  the region 0≤x≤4,0≤y≤1

Q: Suppose that f(x, y) = 8x + 4y and the region D is given by {(x, y) | –1< x < 1, – 1 <y< 1}. D Then…

A:

Q: ) Evaluate Sxy dx dy R is the region bounded by x =0, x =2, y = x

A:

Q: SSR √√(x − 1)² + (y − 1)² dxdy

A:

Q: Evaluate the double integral 4 = SS R y2 dædy over the region R={(x,y)|0 < x < 4, 1 < y < 4 }

A:

Q: Calculate the following triple integral:   ∭T xy sen(yz) dxdydz , where T is the region bounded by…

A:

Q: Integrate f(x, y) = x over the region D bounded by y = x2 and y = 6x + 7 x dA 1152

A: According to the given information, it is required to integrate the function f(x,y) over region D.

Q: integrate ƒ over the given region. ƒ(x, y)  = y cos xy over the rectangle 0&lt;= x &lt;= pai, 0…

A: Given, f(x, y) = y cos( xy ) and we have to calculate integrate this function over the given region.

Q: Consider calculating the size of the region = {{x, y) E R² : y > V3x², æ² + y? < 4}, with the 2d…

A: we have to find out  upper and lower limits of  y and x integral for the following given function…

Q: Evaluate the double integral S, x dx dy where the region R is bounded by: R 9. y = 4x – 3, y =x +, y…

A:

Q: If 'V' is the region bounded by the planes x = 0, x = 2, y = 0, z = 0 and z+y = 1 then the value of…

A:

Q: Evaluate the 2d integral Sla ydædy, where the region 2 is defined N:= {(x, y) E R² : 0 < x < 7, sin…

A:

Q: Evaluate the double integral 4 = SS*, dzdy Ry2 over the region R={(x,y)|1 < x < 4, 4 < y < 8 }

A:

Q: Calculate the double integral ∬Rxy2dxdy over the region R= {(x,y)|1≤x≤5, 0≤y≤2}.

A:

Q: Suppose that f(x, y) and the region D is given by {(x, y) |1< x < 2, 2 < y < 4}. Then the double…

A:

Q: Evaluate the triple integral over the indicated bounded region E. x dv, where E = {(x, y, z)| –8 < x…

A: Topic = Application of integration

Q: Evaluate the triple integral / (x + y) dV over the bounded region E E = {(x, y, z)|0 < x < y – 1, 0…

A: Simplify the given integral using the given boundary conditions. Then integrate using the properties…

Q: Write an iterated integral for Slp f(x, y) dA, where the region 4. D is bounded by the phs of y= 2,…

A:

Q: Ise an iterated integral to find the area of the region. dy dx = Jo y 8 7 6 5 3 2 -1 4 7. 8

A: We want to find area shaded in diagram.

Q: (d) If R is the region bounded by y = x² and y = 2x² – 4, then | S(x, y) dA as R an iterated…

A: Given, y=x2y=2x2-4

Q: Calculate the double integral (ir + 4y + 24) dA where R is the region: 0 <x < 2, 0<y< 3.

A: we have to find the following double integral

Q: Calculate the double integral ∫∫R xcos(2x+y)dA where R is the region: 0≤x≤π/6, 0≤y≤π/2

A: the double integral ∫∫Rxcos(2x+y)dA where R is the region: 0≤x≤π/6, 0≤y≤π/2