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Chapter 15 Solutions
Multivariable Calculus
- 48. Use spherical coordinates to evaluate x² + y? + z? dz dx dyarrow_forwardEvaluate the integral by changing to spherical coordinates. 2 - x2 -y2 16 x2 4 yz dz dy dx 0 10 x2 y2arrow_forwardEvaluate the integral by changing to spherical coordinates. V 16 - x2 32 - x2 - y2 yz dz dy dx x²+ y2 + y2arrow_forward
- 1 1/² x² + y² + z² and evaluate it. (Think about why converting to spherical coordinates makes sense.) 3. Convert the integral √4-x² 4-x²-y² dz dy dx to spherical coordinatesarrow_forwardConvert the integral to spherical coordinates and evaluate it. r5 25 —г2 5+/25-x2-y2 V Va? + y? + z² dz dy dx 25-x2 5- (25–x²-y²arrow_forwardWhat equation do I use for an integral of a rotating triangle?arrow_forward
- Evaluate 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_forwardEvaluate the integral by converting to polar coordinates. /8-y? 1 dx dy = V1+x² + y²arrow_forwardUse Fubini's Theorem to evaluate .2 -dx dy. I + xyarrow_forward
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