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Chapter 15 Solutions
CALCULUS EARLY TRANS.LLF W/WEBASSGN CODE
- Evaluate the integral by changing to cylindrical coordinates. V16 - x 2 16 - x2 - y2 4 x² + y² dz dy dx -4Joarrow_forwardEvaluate the integral by changing to cylindrical coordinates. V4 - y2 xz dz dx dy V4 - y2'Vx? + y2arrow_forwardEvaluate the integral by changing to spherical coordinates. 2 - x2 -y2 16 x2 4 yz dz dy dx 0 10 x2 y2arrow_forward
- Evaluate the integral by changing to spherical coordinates. V 16 - x2 32 - x2 - y2 yz dz dy dx x²+ y2 + y2arrow_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_forwardEvalute the following integral by changing to cylindrical coordinates. 36-3x²-3y² 36-x² L. I ³*-* Ϻ √x² + y² dz dy dx 2arrow_forward
- Use Fubini's Theorem to evaluate .2 -dx dy. I + xyarrow_forwardFind a. a. Əw ?x and b. y Əw dx (2л, -2,-2) = Əw at the point (x,y,z) = (2₁, -2,-2) if w = x² + y² + z² and y sin z + zsin x = 0. əz y (Type an exact answer, using as needed.)arrow_forwardEvaluate the iterated integral by changing to cylindrical coordinates. V16 - x (x²+ y?)3/2 dy dx dz 2 -v16 -arrow_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_forwardEvaluate the integral by changing to cylindrical coordinates. V 16 – x2 r 16 – x2 - y2 x² + y2 dz dy dxarrow_forwardEvaluate the integral below by changing to spherical coordinates. 81 - v2 V 81 - x2 - v2 (x²z + y?z + z³ ) dz dx dy V 81 - y2 V 81 – x2 - y2arrow_forward
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