help QUESTION 14 1 points Save Answe Use spherical coordinates Evaluate JJD Eval

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QUESTION 14 1 points Save Answe Use spherical coordinates Evaluate JJD Evaluatell,(«+r).arwhere B is the ball with center the origin and radius 5 a. 312500 b.4374 c. 4374 o d 559872 e. None of these QUESTION 15 1 points Save Answe Use spherical coordimaes to av. ,./xa+ya+za dr, where Bis the ball xa+ya +247 , where 8 is the balls7 Use spherical coordinates to evaluate2 ++dv b.343 C. 686 @d.2401 QUESTION 16 1 points Save Answe Use a trple integral to find the volume of the solid bounded by x y2 and the planes z 0and x +z»3 a. 183 Ob. 11.3 c.15.3 od.2.5 #83

Explanation / Answer

Solution:(14)

In spherical, the ball B is expressed as

B = {(,,) 0 5,0 2,0 }.

The integrand(x^2 + y^2 + z^2)^2 is simply ^4 in spherical coordinates, and so our integral is

(x^2 + y^2 + z^2)^2 dV
= ( = 0 to 2) ( = 0 to ) ( = 0 to 5) ^4 (^2 sin d d d)
= 2 [( = 0 to ) sin d] * [( = 0 to 5) ^6 d]
= 2 * 2 * 78125/7
= 312500 / 7. Answer is A.

Solution:(15)

Converting the integral to spherical coordinates:
(x^2 + y^2 + z^2) dV
= ( = 0 to 2) ( = 0 to ) ( = 0 to 7) * (^2 sin d d d)
= ( = 0 to 2) d * ( = 0 to ) sin d * ( = 0 to 7) ^3 d
= 2 * -cos {for = 0 to } * (1/4)^4 {for = 0 to 7}
= 2 * 2 * (2401/4)
= 2401. Answer is D.

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