Let J = √x² + y2 + z² dV, Where E is the region given by : E x² + y² + z² ≤2 Expressed in Spherical Coordinates (p, , 0), the integral J is equivalent to : 2π -π/2 1²² 1/² 1/2 p²sin(p) dp do de 0 0 -2 2 p²cos(p) dp do de π 0 2π π/2 √2 p*cos(p) dp do de √₂ p³cos(p) dp do de 0 0 -√2 2π √2 offr Sp³sin(c) dp do de 0 0 0 T 0 0 0 0 T S™

Q: Use spherical coordinates to evaluate /R Vx2 + y² + z² dV , where B is the ball x² + y? + z? < 10 В

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Q: Use spherical coordinates to evaluate x² + y² + z² = 36. I x² + y² dV, where E is the region between…

A: is the region between the spheres and .We have to find .

Q: Use spherical coordinates to evaluate 2π FT S 2-r r+z 0 (r² +2²) ³/ rdz dr de.

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Q: 4. Use spherical coordinate system to find the area of the strip as0SB on the spherical shell of…

A: Given Strip α≤θ≤β on the spherical shell of radius awhen α=0 and β=π

Q: For an area A in the x-y plane, in the expression I₂ = Ix+ly, the term /₂ is the: Minimum…

A: Introduction : As per definition, The polar amount of inertia is the total sum of the moment of…

Q: luate the surface integral. // (x + y + z) ds, S is the parallelogram with parametric equations x =…

A: Sub x= u+v  y= u-v  z= 1+2u+v

Q: 2. Rewrite the integral using spherical coordinates. Do Not Evalu- ate. ·3 9-y² √x_-3√x= -√√9-3²).…

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Q: By changing to polar coordinates, evaluate the integral where D is the disk x² + y² ≤ 36. Answer= (x…

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Q: By changing to polar coordinates, evaluate the integral ∬D (x2+y2) 3/2 dxdy where D is the disk…

A: Given integrand is ∬Dx2+y232dxdy where, D is the disk x2+y2≤49 We have to evaluate ∬Dx2+y232dxdy…

Q: Through polar coordinates, evaluate ∬cos(x2+y2)3/2dA  where R is the region enclosed by equations…

A: Polar coordinates are related with cartesian coordinates with the following relations x=r cosθy=r…

Q: Use pola

A: Introduction: To convert the rectangular coordinates x,y into the polar coordinates r,θ, we have,…

Q: 2. Let W be the region where x2 + y? + z2 2. Use spherical coordinates to find I (2? + y? + 2?)-i…

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Q: Use spherical coordinates to evaluate fff (9-x² - y2) dV where E is the solid hemisphere E x² + y2 +…

A: To Evaluate: The integral ∫∫∫E9-x2-y2dV where E: x2+y2+z2≤9 , z≥0 using spherical coordinate system.

Q: line integral x³ dy), where y is t 3 X counter clockwise.

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Q: Use cylindrical coordinates. Evaluate JIS. √x² + y² dv, where E is the region that lies inside the…

A: Evaluate the integral.

Q: 5. Use spherical coordinates to evaluate the triple integral ///+y²+²dV, where E is the ball: x? +y?…

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Q: 4. Convert the integral from Cartesian coordinates to both cylindrical and spherical coordi- 1-T²…

A: The given problem is to convert the given triple integral in Cartesian coordinates to triple…

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

A: Use spherical coordinates to evaluate the triple integral SSSE x2 + y2 + z2 dV, Where E is the ball:…

Q: Evaluate the surface integral. (x + y + z) dS, S is the parallelogram with parametric equations x =…

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Q: Use spherical coordinates. SIL Evaluate (x2 + y2) dv, where E lies between the spheres x² + y2 + z²…

A: Consider the given integral ∫∫∫Ex2+y2dV, where E lies between the spheres x2+y2+z2=4  and…