By changing to polar coordinates, evaluate the integral ∬D (x2+y2) 3/2 dxdy where D is the disk x2+y2≤49 Answer =

Q: By changing polar coordinates, evaluate the integral to where D is the disk x2 + y < 4.

A: Explanation of the answer is as follows

Q: Y – 5x |dA 100 cos x + y

A: We have to evaluate the double integral ∬100cosy-5xx+ydxdy over the region D where the region D is a…

Q: Evaluate the line integral -y dx + z dy + 2x dz, where C is the helix by 7(t) = (cos t, sin t, t),…

A:

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

A:

Q: Evaluate the given iterated integral by converting to polar coordinates. 22 Vx² + y² dy dx

A: First of all, consider the upper limit for the integration w.r.t dx. Rearrange the expression to get…

Q: Evaluate the line integral [6. 6ayⓇ ds, where C is the right half of the circle x² + y² = 4.

A: To evaluate :   ∫C6xy6ds, where C is the right half of the circle x2+y2=4 Prerequisite : We can…

Q: Evaluate the spherical coordinate integral. 1- cos 2 2x x SS S p²sin dp do de 00 1- cos 2 2x x SS S…

A:

Q: The speciat sotution to the equatio %3D ho A/y)=+X B/yo)=y - %3D d/other than that

A:

Q: Change the Cartesian integral to an equivalent polar integral, and then evaluate. S LvS- (x² + y²)…

A: Solve

Q: Evaluate the integral by converting to polar coordinates: a x²y dædy 0 -va?-y2

A: Given ∫0a∫-a2-y20x2ydxdy Evaluate integral by converting to polar coordinates Green curve is the…

Q: evaluate the integral where c circle of positive rotation e^z/1 -cos(z) dz where C is |Z |= 1

A:

Q: Integrate ƒ(x, y) = sqrt(4 - x2) over the smaller sector cut from the disk x2 + y2 &lt;=4 by the…

A:

Q: Evaluate the given integral using the Cauchy Integral Formula or theorem. ez dz z2 – 9 - where y is…

A:

Q: Use Green's Theorem to evaluate the line integral f(e*c - 2y)dx+(5x+ev* dy, where C is the 15. 2cos:…

A: We need to find integral.

Q: Find the area of the surface generated by eY + e -y revolving the curve x = in the interval -In 2…

A:

Q: Evaluate the line integral 32xy ds, where C is the portion of the parabola y = x² from (-1,1) to…

A:

Q: Convert the integral 9-x²-y? Vr2 + y² + z² dzdydx to spherical coordinates then evaluate.

A: Consider the triple integral         I=∫03∫09-x2∫09-x2-y2x2+y2+z2 dz dy dx in cartesian coordinates.…

Q: Use polar coordinates to find the integral 16 - x² - y? dx dy where R is the circle x? + y? < 4.

A:

Q: Evaluate the iterated integral by converting to polar cooordinates. ∬(e−x2 − y2 ) dy dx limits of…

A:

Q: (2) Use the transformaiton u = xy, v = x² – y? to find JJ (æ* – y*)e*³ dA where R is the region in…

A: Given: The region bounded by the hyperbola xy=1 &amp;3, x2-y2=3 &amp;4 Where u=xy and v=x2-y2

Q: Evaluate the following. dV where R is the portion of the ball of radius 1 in 4-dimensions with all…

A: We need to evaluate the value of integral in 4 dimensions.

Q: Compute the line integral -xdy + ydx 2(x-y)2 + 4xy where L is the circle (1-x)2 + y? 3 with a…

A: We will find parametric equation of L and then convert whole equation in parametric form

Q: Q.1) Use the polar integral to evaluate 2 dydr 71+ Vr2 + y?

A:

Q: Y – 5x |dA x + y 100 cos

A: We have to evaluate the double integral ∬ 100cosy-5xx+ydxdy over the region D where D is the…

Q: Evaluate the line integral (cos x + sin y) ds; C is the line segment from (0, 0) to (x, 67).

A:

Q: The double integral I = f,*S* x² +y² dydx in polar coordintes is:

A: We have to solve the problem of double integration. ∫13∫1xx2+y2dydx In the polar coordinates,…

Q: Consider the solid whose base is the region bounded by 4x? + 9y? = 36. Y 3 -3 -2 -1 -1 2 3 2 -3 1.

A:

Q: Evaluate the triple integral (* + 1y) dV where E is bounded by the parabolic cylinder y = 32² and…

A: We have to find the triple integral  ∫∫∫E(x+y)dVwhere E is bounded by the parabolic cylinder y=3x2…

Q: Use polar coordinates to evaluate the double integral V1 1-z2 dy dæ. (1+z² + y?)²

A:

Q: When transforming the triple integral V9-x2 (x2+y2 +z?) dzdvdx 2n n 3 to spherical coordinates…

A:

Q: Use Green's Theorem to evaluate the following line integral. Of dy -g dx, where (fg) = (7x2,8y?) and…

A:

Q: Change the Cartesian integral to an equivalent polar integral, and then evaluate. Nan 72 - y² Z+y²…

A:

Q: Calculate (1+ cos(y²))dA,where D is the triangular region with vertices(0, 0). (–2 - Vĩ,2· VT) e (0,…

A: Given problem:- The given integral is ∫∫D1+cosy2dA, where D is the triangular region with vertices…

Q: Evaluate the following triple integral by changing to spherical coordinates. /8-x²-y² (1² + y² +…

A:

Q: Use either form of Green's Theorem to evaluate the following line integral. 03x y dx+ 4x y dy; C is…

A: According to the given information, it is required to find the value of integral using Green’s…

Q: Evaluate the double integral cos V x2 + y?dA, where D is the disc with center the origin and radius…

A: See the details solution in below

Q: Evaluate the given integral by changing to polar coordinates. ∫∫D  2x2y dA, where D is the top half…

A: In the question it is asked to solve double integral using polar coordinates.

Q: Evaluate the line integral Sa y dx +z dy, where C is the line segment from (4) (-1, 1, 2) to (2,3,…

A:

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: Evaluate the given integral using the Cauchy Integral Formula or theorem. i – z2 -dz 10 – 7z + z2…

A:

Q: Find the area of the part of the plane defined by 3z + 2y + z 12 that lies in the first octant.

A: Given equation of plane :  3x+2y+z= 12

Q: Evaluate the double integral. 8y2 dA, D is the triangular region with vertices (0, 1), (1, 2), (4,…

A: we have to find given double integral

Q: Evaluate the line integral, where C is the given plane curve. xy ds, C is the right half of the…

A:

Q: Evaluate the double integral /.2 5dA, 3. +y² where R is the region that lies between the circles…

A: Given ∫∫Ry2x2+y2dA  where R is region lie between the circles x2+y2=16 and x2+y2=49

Q: Evaluate the given integral using the Cauchy Integral Formula or theorem. z2 +1 dz z - 2 | where y…

A:

Q: Use the polar coordinates to evaluate volumes : 2) Below z = V1- x2 – y2 inside x² + y2 = above the…

A: Using the polar coordinates we have to evaluate the volumebelow z=1-x2-y2 inside x2+y2=14 above xy…

Q: Compute the double integral // Vx² + y² dA where D is the part of the first quadrant lying between…

A:

Q: Calculate the double integral ∬R(x2+y2)dxdy in the circle x2+y2=2x.

A: Write the equation of circle into standard form. The radius of the circle is 1.

Q: By changing to polar coordinates, evaluate the integral where D is the disk x² + y² ≤ 25. [][₂₁x² +…

A: