Calculus Disk/Washer Method for VolumeI am given the bounded functions y = l n ( x ) , g ( x ) = − .5 x + 3, and the x-axis. The reigon R is bounded between these, and I'm tasked with finding the volume of this solid using disk/washer method when revolved around the x-axis.I know the formula I need to use, but I'm a little confused on finding the upper and lower limits and which to place as an innner and outer radius since the functions aren't graphed like the traditional washer method problem.

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Calculus Disk/Washer Method for VolumeI am given the bounded functions   y  =  l  n  (  x  )  ,  g  (  x  )  =  −  .5  x  +  3, and the x-axis. The reigon R is bounded between these, and I&#039;m tasked with finding the volume of this solid using disk/washer method when revolved around the x-axis.I know the formula I need to use, but I&#039;m a little confused on finding the upper and lower limits and which to place as an innner and outer radius since the functions aren&#039;t graphed like the traditional washer method problem.

dkmc4175fl · Accepted Answer

Step 1The region you described is the shaded region in the graph. Note the three intersection points. These points are of interest:1.       x    0  , the intersection of   y  =  l  n  (  x  ) and   y  =  0 (x-axis)2.       x    1  , the intersection of   y  =  l  n  (  x  ) and   y  =  −  0.5  x  +  33.       x    2  , the intersection of   y  =  −  0.5  x  +  3 and   y  =  0.Step 2This splits the region into two subregions.1. The left subregion from   x  =      x    0   to   x  =      x    1   (i.e.       x    0    ≤  x  ≤      x    1  ). Also   0  ≤  y  ≤  l  n  (  x  ).2. The right subregion from   x  =      x    1   to   x  =      x    2   (i.e.       x    1    ≤  x  ≤      x    2  ). Also   0  ≤  y  ≤  −  0.5  x  +  3.Correspondingly, you need to perform two definite integrals (one for each subregion). Let r denote the inner raidus and R denote the outer radius.1. The first definite integral has a limits of integration       x    0   and       x    1   and uses   r  =  0 and   R  =  l  n  (  x  )2. The second definite integral has a limits of integration       x    1   and       x    2   and uses   r  =  0 and   R  =  −  0.5  x  +  3

Given the bounded functions y=ln(x), g(x)=-.5x+3, and the x-axis. The reigon R is bounded between these, and I'm tasked with finding the volume of this solid using disk/washer method when revolved around the x-axis.

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