Finding volume of a washer via integrationObjective: Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Sketch the region, the solid, and a typical disk or washer. y = x 2 , x = y 2 ; rotated about y = 1.I know how to sketch the graph. I assumed the integral would be: π ∫ 0 1 [ ( x 2 ) 2 − ( x ) 2 ] d xI checked the solution and it's actually: π ∫ 0 1 [ ( 1 − x 2 ) 2 − ( 1 − x ) 2 ] d xI know this must have something to do with the rotation about y = 1 but that's it. Would the integral be: π ∫ 0 1 [ ( 1 + x 2 ) 2 − ( 1 + x ) 2 ] d xif I were to rotate it by y = − 1? All answers will be appreciated.

Question

Finding volume of a washer via integrationObjective: Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Sketch the region, the solid, and a typical disk or washer.  y  =      x    2  ,   x  =      y    2  ; rotated about   y  =  1.I know how to sketch the graph. I assumed the integral would be:  π      ∫    0    1    [  (      x    2        )    2    −  (      x        )    2    ]    d  xI checked the solution and it&#039;s actually:  π      ∫    0    1    [  (  1  −      x    2        )    2    −  (  1  −      x        )    2    ]    d  xI know this must have something to do with the rotation about   y  =  1 but that&#039;s it. Would the integral be:  π      ∫    0    1    [  (  1  +      x    2        )    2    −  (  1  +      x        )    2    ]    d  xif I were to rotate it by   y  =  −  1? All answers will be appreciated.

andytronicoh4t · Accepted Answer

The common ratio is simply the number that each number is being multiplied by to find the next term.For example, when the sequence goes 4,12, 4 is being multiplied by 3.When the sequence goes from 12 to 36, 12 is being multiplied by 3.This is true for the entire sequence.The term following 108 will be       108    ×    3    =    324  The term proceeding 4 will be             4      3       since             4      3        ×    3    =    4

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Sketch the region, the solid, and a typical disk or washer. y=x^{2}, x=y^{2}; rotated about y=1.

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