Jraen fusk hon conespaaday to o d'u z ul) = flx). dx² Find the the egualido for conespoodiang to with boundary condibions ule) =o and ul1) =VO.

Q: Evaluate the iterated ntegral by Lonverting to polor coordinates. 2. zy dx dy 34

A:

Q: Evaluate the line integral fc (2 + x*y)s, where C is the half circle x + y? = 1 in the upper half…

A:

Q: Hiw Enadunte SSS where s is the selid bounded the Śur faces

A: Given - S is the solid bounded by the surfaces x2 + y2 = z2, z = 0, z = 1 To find - Evaluate ∭Sx2 +…

Q: Evaluate ze dV, where E is the portion of the ball centered at the origin of radius 5, x + y+< 25…

A: Given Where E is portion of the ball centered at origin, radius 5 and lies in first octant. In…

Q: Evaluate f, A.n ds, where A = zi +j- 3y²zk and S is the surface of cylinder x? + y? = 16 included in…

A:

Q: find the ora of the Region described t vegion bounded by gee"iy=e EIny and

A:

Q: Find the area of the part of the plane  z = ax + by + c  that projects onto a region in the…

A:

Q: TYz dS; C:r= 2sent, y = t, z = -2cost.

A:

Q: Calculate the line integral ∫Cy2ds, where C is a part of the circle x=acost, y=asint, 0≤t≤π/2.

A:

Q: 13-Evaluate JSS zdV E where E lies between the spheres x2 + y? + z² = 1and %3D x? + y? + z? = 4 in…

A:

Q: Evaluate ze*²+y²+z? dV, where E is the portion of the ball centered at the origin of radius 5, x2 +…

A:

Q: Use Green's theorem to evaluate the line integral frdx + (a - 20)dy where C is the boundary of the…

A:

Q: Consider the solid that is bounded above by x² + y? + z? = 169 and below by z=5. %3D

A: In this question, we have to write the triple integral to find the volume of the solid bounded by…

Q: Apply Stoke's theorem to calculate S. (x + y – 4)dx + (2x – z)dy + (y + z)dz, where C is the…

A:

Q: Use Green's theorem to evaluate O(1-y') dx+(x³ +e" ) dy , where C is the boundary of the region…

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

Q: Evaluate the integral eiz dz, (22 + 1)2 where C is the circle |2 + il = oriented anticlockwise.

A:

Q: Use green's theorem to calculate the integral Fdr, F(r, y) = (e* + x²y , e³ – ry² + sen(3) + 2)…

A:

Q: |Use Green's Theorem to evaluate | -x'ydx+xy°dy where C is the boundary of the C circle x + y =16…

A:

Q: Q:4) Use Green theorem and evaluate the line integral ${Mdx + Ndy} Where M(x,y)=y², N(x,y)=x², C is…

A: See the details solution in below

Q: Evaluate the line integral So 7y dr + 3x dy where C is the straight line path from (2, la 7uda + 3z…

A: Introduction: A line integral is an integral that determines the function to be integrated along a…

Q: Find thequahen. perpenditar to i fine -個 epe at OD pr Find tha liit ultpy cen gale (ro a) Po FO…

A:

Q: Use Greens Theorem to evalua te the line integral Sr -93 dx +x*dy. where C is the positively onented…

A:

Q: 7. Which surface is parameterized by ř(u, v) = (u, uv, v) for –1 < u <1 and –1< v< 1?

A: r→(u, v) = u, uv, v for -1≤u≤1 and -1≤v≤1The parametric curve is  Option C is correct.

Q: Compute where Cis the counter clockwise oriented boundary of upper-half unit disc D. 0.66666666667…

A: We need to find ,  ∮ y2dx + 3xydy , over  C ,  where C is the counter clockwise oriented boundary of…

Q: | Let C be the quarter circle centered at (2,0) that goes from (1,0) to (2, 1). Evaluate the…

A: ∫c y2xdx + 4yxdy=? We know that this form of integral is solved by Green theorem: ∮cP dx+Q…

Q: If the region R is bounded between two circles 961 x² + y? = 4, x² + y? then we have: 2л 3 sin(Vx2 +…

A:

Q: 4. Evaluate the line integral / r y* ds where C is the right half of the circle r² + y² = 16.

A:

Q: 8. Evaluate ze+y´+z² dV, where E is the portion of the ball centered at E the origin of radius 5, x?…

A:

Q: Use geometry to evaluate ∫∫∫R 1 dV where R is the region inside the sphere x2+y2+z2=4.

A: Given R as the region inside the sphere

Q: 1 Evaluate dV, where E lines between the spheres a? + y? + z² = 25 and %3D x² + y? + z2 49 in the…

A:

Q: consider surface s with parami Glusv) = cu vo uv) Compute Pa, 7 Nas Tu, Tv o of s olso compute the…

A: Given surface is, G(u,v)=(u,v,uv)

Q: 2 Use Green's Theorem to evaluate Jx*ydx-xy dy, where C is the circle 2+ y? – 2601 with…

A: Let be the vector field and C be the boundary of the region D. The Green's theorem states that .

Q: Find The or rthoganal tajeclolies. ! d faly Curver r= 4C cose, where C be being parameer

A:

Q: Find the integral fc ez dz where C is the circle |z| = 3 in CCD. (z – 1)2(z – 2) %3D -

A:

Q: 6- Evaluate the line integral fF - dr, where F = [ry, yz, xz] and C is the boundary of the…

A:

Q: 3. Please give clear explanations

A: The parametrization of a surface S is given by       G(u, v)=(u, v, uv) where D is u2+v2≤1.

Q: Evaluate the line integral fx ds between (4,0) and (0,4), where C is the circle of radius 4 centred…

A:

Q: (1) Compute where Cis the couater dockwise oriented boundary of upper half unit disc D.

A: It is given that, ∮Cy2dx+3xydy here C is counter clockwise oriented upper half disc D.   Here,…

Q: Evaluate the line integral |(2? + y) dx – x dy where C is the line segment from (2,5) to (5,9) in…

A:

Q: Use Green's Theorem to evaluate (1in z – 2y) dz + (x – ycos y) dy, where C is the circle (x – 4)² +…

A: Given: C is the circle x-42+y-42=9. ∮Cxsinx-2ydx+x-ycosydy. To find: Using Green's theorem, value…

Q: Compute the line integral f, x?dx + y²dy where the path C consists of the arc of the circle x? + y?…

A: Here we solve the given problem of integral.

Q: Use green's theorem to calculate the integral Fdr, F(x, y) = (e* + a²y , e" – xy² + sen(y) + 2)…

A:

Q: B is the first quadrant part of the region enclosed by the circles x2 + y? = a? and x2 + y? = b2…

A:

Q: Let B be the ball with center at the origin and radius 1 SIS 4(z² + y² + z*)dv = B

A:

Q: Evaluate the line integral Levis where C is the half circle x² + y² = 1, y ≥ 0. x² + y² ds

A:

Q: Evaluate dV, where E lines between the spheres a+ y + z = 9 and E 2 + y2 + z? x2 + y? + z2 = 16 in…

A: The answer is in step 2

Q: the line integral SexY² ds where C is the of the Circle x² + y²=4 oriented clockwise Evaluate Cight…

A: