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Chapter 13 Solutions
Calculus: Early Transcendentals (2nd Edition)
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- + 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_forwardConverting 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_forward(2) Evaluate the iterated integral by converting to polar coordinates. IT 2 V8-y? || Vx² + y² dx dy o yarrow_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_forward14. 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
- 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
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