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Chapter 13 Solutions
Calculus: Early Transcendentals, 2nd Edition
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- Converting from Rectangular Coordinates to Spherical Coordinates Convert the following integral into spherical coordinates: y=3 x=√√9-y²z=√√/18-x²-y² , , x=0 y=0 [ (x² + y² + z²) dz dx dy. z=√√/x² + y²arrow_forwardFind using spherical coordinates integration z?Vz? + x2 +y?dzdydxarrow_forwardV4 - x2 8- x2 – y 2 Convert the integral dz dy dx into an integral in spherical coordinates and evaluate it. x2 Vx2 + y2 dp dp de Derarrow_forward
- + y? Evaluate the integral by changing to spherical coordinates. x2 V 72 - x2 – y2 36 xy dz dy dx x² + y? Need Help? Watch It Read Itarrow_forwardFor an area A in the x-y plane, in the expression I₂ = 1x + ly, the term /₂ is the: Minimum rectangular moment of inertia or second moment of area. O Product of inertia. Polar moment of inertia. O Maximum rectangular moment of inertia or second moment of area.arrow_forward(2) Evaluate the iterated integral by converting to polar coordinates. IT 2 V8-y? || Vx² + y² dx dy o yarrow_forward
- 14. Convert the integral to spherical coordinates and evaluate the integral. V49 - x? V49 – x2 - y? 7 x² + y 2 + z dzdydxarrow_forwardChanging an Integral from Rectangular to Spherical Coordinates 2 O So S" Só (p² sinp)dpdpd0 O F S2 So (p² sinp)dpdpd® 2x O fr S S ? (6² sinp)dpdpd0 O " So2 S (p² sinp)dpdpdOarrow_forward√1-x² [²₁²³ [" (2²³ + 1²³) dz dy de to cylindrical coordinates and L evaluate the result. (Think about why converting to cylindrical coordinates makes sense.) 2. Convert the integralarrow_forward
- 33. Rectangular to spherical coordinates (a) Convert to spherical coordinates. Then (b) evaluate the new integral. Vī-x² dz dy dx |-Vi-x²J Vr+y²arrow_forwardEvaluate the integral by changing to spherical coordinates. V1- (23 + xy² + æz² ) dz dy dæ Select one: а. 4 O b. 6 O c. 12 O d. 57 16 37 O e. 8arrow_forwardDetermine the y-coordinate of the centroid of the area under the sine curve shown. y y = 3 sin 11 3 --x 11 Answer: y = iarrow_forward
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning
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