- Evaluate the integral 4-z²-y² 1 dz dy dx Jo 4-z²-y² x² + y² + 2² using spherical coordinates.

Q: When transforming the triple integral a-st-y" (xZ+ y² + z²)ể dzdydx . 9-x2 9-X 2n n 3 to spherical…

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Q: Convert the following integral to spherical coordinates: 8-x²-y² I = dz dy dx -2 J-V4-x² J V æ²+y²

A: We have to convert the given integral to spherical coordinates.

Q: 5. Evaluate the integral (z²² + y² + z²)³/²dzdydx by changing rectangular coordinates to spherical…

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Q: 4–x²-y² By using spherical coordinates, evaluate the integral x dz dy dx

A: Given integral is ∫01∫-1-x20∫z=04-x2-y2xdzdydx The objective is to evaluate the integral using…

Q: Convert the given integral into an integral in spherical coordinates. /16-х° 16- x (x² + y? + z?)²…

A: Convert the given integral.

Q: Evaluate the line integral rye dy where C has parametric equations y = t 2 = x =t 0st<1.

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Q: Set up the integrals I| æ dV in spherical coordinates, where D is the solid that lies between the…

A: From the given problem;   ∫∫∫DxdV So, ∫∫∫xdV=∫∫∫xdxdydz   Now change into cartesian to spherical…

Q: Use spherical coordinates to evaluate the triple integral x² + y² + z² dV, where E is the ball: x² +…

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Q: /2x-x² •3 z Vx² + y² dz dy dx. 0.

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Q: In spherical coordinates, the integral equivalent to None of these. 2πT π/2 2 S 6,²¹² 6² p² sin…

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Q: When converting the triple integral to spherical coordinates, it becomes of the form V9-x² -y² vターx。…

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Q: 7. Evaluate, in spherical coordinates, the triple integral of f(p,0, 0) = cos 0, over the region 0 <…

A: Answer is 3√3π .

Q: Change the Cartesian integral to an equivalent polar integral VI-x² e-(x²+y²) dy dx O re-r re dr dt…

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Q: Evaluate the cylindrical coordinate integral. 1/2 18 1/r cos 0 dz r dr d0 0 9 1/?

A: Given that triple integration problem or cylendrical coordinate problem .we use simple integration…

Q: Change the iterated integrals to spherical coordinates 1 VI-x VI-x-y? x²-y? 1 dzdydx x2 + y2 + z2 -1…

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Q: ارو رهجہ 10. Change dz dy dx into spherical coordinates and evaluate the integral. -1 0

A: ∫-11∫01-x2∫01-x2-y2e-x2+y2+z232dz dy dx To Find: Change the given integral into spherical…

Q: 3) Convert the following triple integrals to cylindrical coordinates or spherical coordinates (do…

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Q: ¹ // x² + y² + 2² dV, where E is the ball: x² + y² + z² ≤ 16. Use spherical coordinates to evaluate…

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

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Q: (b) Let E = {(x, y, z) : –1< # < 0, 0 < y < VI– a², 0< z< 2}. Write the integral II| cos (2² + y°)dV…

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Q: Evaluate the spherical coordinate integral. 10x z (1- cos p) /2 p2 sin o dp dp d0 0 0 (1- sin )/2 O…

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Q: 3) Evaluate the cylindrical coordinate integrals in: 2n 1 1/2 ISPsin'e + z") dz r dr de e-1/2

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Q: 36. Convert the integral •Vī-y² (x² + y²) dz dx dy Jo to an equivalent integral in cylindrical…

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

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Q: Convert 18-22-y2 22 +y? +z dz dz dy into spherical coordinates. Hence evaluate the integral.

A: The volume of a solid can be calculated using the triple integrals in the spherical coordinates. The…

Q: Evaluate the triple integral J]¸ 1 dV in cylindrical coordinates, where E - ((r, e, z)|0Srs 1,0 s es…

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

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Q: Use cylindrical or spherical coordinates to evaluate the integral. 4-y² /8–x²-y² 19. z? dz dx dy 0.…

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Q: When transforming the triple integral 9-x 9-x2-y- (x² +y² +z?)% dzdydx 2n n 3 to spherical…

A: Triple integral conversion to special coordinates

Q: 3) Evaluate the cylindrical coordinate integrals in: 2n 1 1/2 || | (r²sin²0 +z²) dz r dr d0 0 0 -1/2

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Q: at Va:-x dz dy.dx

A: To convert the integral  ∫-aa∫-a2-x2a2-x2∫aa+a2-x2-y2zdzdydx to spherical and cylindrical…

Q: 10. Use polar coordinates to evaluate the integral -s* drdy D= {(r, y) € Rlz² + y² > 9}

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Q: 4-z2-y2 By using spherical coordinates, evaluate the integral a dz dy dr

A: Consider the integral ∫01∫−1−x20∫04−x2−y2xdzdydx We have to evaluate the given integral by using…

Q: b) Evaluate the following triple integral by using spherical coordinates. 4 V16-x2 32-x2-y2 I = (3x²…

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Q: 5. Evaluate the following integral using spherical coordinates: 2-x²-y² ста z dz dy dx. x² + y²

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Q: Convert the given integral into an integral in spherical coordinates. V81 V81 - x- - y2 (x2 + y2 +…

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Q: Evaluate the following integral in spherical coordinates. C[le-(4x2 + 4y² + 4z²) °/² dV; D is a unit…

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Q: 7. Use spherical coordinates to find ||| z dx dy dz where E is the solid defined by E Os Vr* +y³ <z…

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Q: 4. Convert the following triple integral into cylindrical coordinates (Do Not Evaluate). 16-r2…

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Q: 3) Convert the following triple integrals to cylindrical coordinates or spherical coordinates (do…

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Q: 2)use the polar coordinates to evaluate the double integral: )x2 +y2 dA R is the disk x2 + y2 < 9 A)

A: We have to use polar coordinates here.

Q: (10) Sketch the solid bounded by z = x2 + y? and z 4- x2 - y². Use cylindrical coordinates to find…

A: Given ∫∫∫Dx2+y2dVand solid bounded by z=x2+y2 and z=4-x2-y2

Q: Change the Cartesian integral to an equivalent polar integral, and then evaluate. (9-x2 3 s S - 3…

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Q: Use spherical coordinates to evaluate the triple integral ∫∫∫E x2+y2+z2 dV, where E is the ball:…

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Q: V4 - x2 8- x2 – y 2 Convert the integral dz dy dx into an integral in spherical coordinates and…

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Q: 7. Use cylindrical coordinates to evaluate S √x² + y² dx dy dz where S is bounded by Z= √√x² + y², z…

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Q: Change the iterated integrals to spherical coordinates 1 y1-z² /1-x2-y2 S V1-z²-y? SS dzdydx…

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