b. $ (xy2 + sin(x + y?)) dx + (3x²y + 2y sin(x + y2))dy where C is the clockwise boundary of the region enclosed by the y-axis, the line 3x - y = 1, and the semicircle y = V5 – x2.

Q: x² sin xy 14.5.8. || - dA(x, y), if D is the region bounded by æ² = "4, x² = TY, y² = ;, and D y? =…

A:

Q: 10. (1 – y³) dx + (x³ + e*) dy, Č is the boundary of the region between the circles x² + y² = 4 and…

A:

Q: Н.W Ql: Evaluate f y* dx - x'dy where C is the positively oriented circle of radius 2 centered at…

A:

Q: The area of the region bounded by the curves 2y2 +2 and z 2y+2 is 2. 3 5 -1 -2 16 17 (A) 3 (B) 3 13…

A:

Q: Evaluate ſf, (3x + 4y²) dA where R is the region in the upper half - plane bounded by the circles x²…

A: As the areas are circular thus convert the integral into polar form. Now determine the limits of the…

Q: Evaluate I = , dx dy where R is the region that lies inside the circle x2 + (y – 2)2= 4 and outside…

A: We have to find ∬Rdxdy where R is the region that lies inside the circle x2+y-22=4 and outside the…

Q: Use Green's theorem to evaluate f, xy?dx + 3 cos ydy where C is the boundary of the region in the…

A: Let R be a region in the xy-plane that is bounded by a closed, piecewise smooth curve C, and let…

Q: The area of the surface generated by revolving the curve y=x² if 0<x<2 about the y-axis is given by…

A:

Q: find the area of the surface S: x² + y² + 2² = 4 -A <tan -^ (*) FO 6 < COS Cos FJ VI (2) 4 DEX TI 3…

A: The given Surface is                    x2+y2+z2=4 ........1where π6≤tan-1yx≤π3 and π4≤cos-1z2≤3π4…

Q: Use Green's Theorem to evaluate Se (y? – tan-1 (r)) dr + (3r + sin (y)) dy, where C is the boundary…

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

Q: (1– y°)dx+(x° +e )dy, where C is the boundary of the region between the circles x2 + y2 = 4 and x2 +…

A: Given integral, ∮C1-y3dx+x3+ey2dy Here C is the boundary of the region between the circles x2+y2=4…

Q: By making a suitable change of variables, evaluate y SS, = dx dy where A is the region in the first…

A:

Q: the surface z = &x + 4y th=

A:

Q: Can you show the steps on how to do this integral?

A: Consider the provided question, (3) Evaluate the integral by using the greens theorem,

Q: Evaluate |[(x+2y)dA,where D is the region bounded by the parabolas y= 2x D and y=1+x².

A: We can help you with the question. I am not sure how to help you with its attachments.

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

A:

Q: /| (x + 2y)dA D.

A:

Q: Q.1B) Prove that: Iff, Cos) dxdy - = sin (1) where R the region bounded by x + y = 1, x = 0, y = 0

A: We use the change of variable to prive the given equality

Q: (1- y*)dx + (x° + e*)dy where C is the boundary of the region between the circles x² + y² = 4 and x²…

A:

Q: Q3/ Evaluate: 1- SS (4x + 2) for the region enclosed by the curves y = x² and y = 2x 2- Show that…

A: 1. Consider a function of two variables, z=fx,y. The double integral of function fx,y is denoted by…

Q: Find c > 0 such that the area of the region enclosed by the parabolas y = x - c² and y = c - z is 1

A:

Q: Evaluate ety - dx + ( 2xy + dy where C is a positively oriented boundary of the region enclosed by…

A:

Q: find the region endlased R by the cunes V=12-2y +1 and Y= -2+2x ャ4.

A: Answer

Q: (b) ( y cos(ry) dA over the region R = {(x, y)|0<x < 1 and 1 < y <7/3}

A:

Q: Find the area of the region enclosed by the curve r = 2+ cos (20). (1.) (3,( Bu Die Aya Yard 97…

A: To find the area of the region enclosed by the curve r=2+cos2θ

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: 2ху dx + (x + у) dy Jc C: boundary of the region lying between the graphs of y = 0 and y = 1 – x2

A: Given: ∫C2xy dx+(x+y)dy y=0 and y=1-x2

Q: $ (ry + sin(r + y²)) dx + (3x²y+2y sin(x + y²)) dy, where C is the clockwise boundary of the region…

A:

Q: x dA; R is the region enclosed by y = sin-' x, %3D x = 1//2, and y = 0.

A: Let I=∬RxdA  We need to evaluate I=∬RxdA over region R enclosed by y=sin-1x, x=12  and y=0

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

A: Given equation is, x2+y2 = z Band cut from the given paraboloid by the planes z = 2; z = 6 Area of…

Q: D be the region that consists of points (x, y) such that x² + (y - 3)² ≤9. Then, (x² + y²) dA equals…

A: see my solution

Q: By a suitable change of variables, evaluate ſf, dx dy where D is the region in the first quadrant…

A:

Q: Evaluate the line integral f. 4y dx + z² dy + (16 – x²) dz over the quarter of the circle of radius…

A: To Determine: Evaluate the line integral over the quarter of the circle of radius 4 in the xz-plane…

Q: T Find the area of the plane region. 0≤x≤ bdunded by y=sin x. x = 2 2 1.111 s.u. π²-4 S.U. 1 s.u. EN…

A: We can solve this using given information

Q: Q7. Use Green's theorem to evaluate y² dx + 3xy dy, where c is the boundary o the semi annular…

A:

Q: (b) Find the area of the surface obtained by rotating the region bounded by the curves 7 35xy 5y12+…

A: To find the area of the surface obtained by rotating the region bounded by the below curves about…

Q: Зу + 7eV X + 7ev x) dx + (10x + 7 cos(y?) ) dy C is the boundary of the region enclosed by the…

A:

Q: S y = 3 – 2 4z – 4 = 3(x +1)?

A: Let us start solving the problem step by step

Q: $(2xy - x²) dx + (x+y²)dy, where C is the enclosed curve of the region boundec. The value of by y=x²…

A:

Q: 4. Find the area enclosed by: a. y= sin(x) and y cos(x), x=0, x = and the y-axis. b. y=x and y =Vx.…

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: The value of $ (2xy - x²)dx+ (x+y²)dy, where C is the enclosed curve of the region bounded by y=x²…

A: As we know from the Green's theorem: ∫CMdx+Ndy=∫∫R∂N∂x-∂M∂ydA   I=∮2xy-x2dx+x+y2dy And C: y=x2, y2=x…

Q: Evaluate y dx+3xy dy, where C is the boundary of the semiannual region D in the upper half-plane…

A:

Q: 4. Find the area of the surface formed by revolving the graph of f(x) = x² on the interval [0,…

A:

Q: (x - y) dv, where E is enclosed by the surfaces z = x² - 1, z = 1 - x², y = 0, and y = 4

A: Consider the given function fx,y,z=x-y.  The region E is enclosed by the surfaces…

Q: The area of the region enclosed byy = 8+|cos , y = 8, z = 27 and z = 117 is

A:

Q: Calculate fSp(3x + 2y) dA where D is the region in the first quadrant that is inside the circle x2 +…

A: NOTE: According to guideline answer of first question can be given, for other please ask in a…

Q: I = Examine the given integral dz ;C z-i -|= 2 the circle

A: