How to calculate the volume of cos(x) around the x-axis and the y-axis separately?I have difficulties finding the right formula how to calculate the volume rotating cos(x) around the x-axis and y-axis separately can you please give me a hint how to do it?The interval is x = [ − π 2 , π 2 ]

Question

How to calculate the volume of cos(x) around the x-axis and the y-axis separately?I have difficulties finding the right formula how to calculate the volume rotating cos(x) around the x-axis and y-axis separately can you please give me a hint how to do it?The interval is   x  =  [  −      π    2    ,      π    2    ]

Caylee Davenport · Accepted Answer

Step 11) Around the x-axis, you get      ∫          −              π        2                            π        2              π  (  cos  ⁡  x      )    2    d  x  =  2      ∫          0                      π        2              π  (  cos  ⁡  x      )    2    d  x,using the Disc method (and symmetry).Step 22) Around the y-axis, you get       ∫          0                      π        2              2  π  x  cos  ⁡  x    d  x, using the Shell method.(Notice that the right half of the region generates the whole solid in this case.)

Leila Jennings · Accepted Answer

Step 1First draw the function. We know that Volume is given by       ∫    a    b    π  f  (  x      )    2    d  x. Therefore       ∫          −              π        2                            π        2              π      cos    2    ⁡  (  x  )  d  x and that&#039;s an easy integral.Step 2While integrating along y axis your function will change to       cos          −      1        ⁡  x and hence integral will become       ∫    0    1    π  (      cos          −      1        ⁡  (  y  )      )    2    d  y