How to calculate the volume of cos(x) around the x-axis and the y-axis separately?I have...

Aleah Booth

Aleah Booth

Answered

2022-07-23

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 ]

Answer & Explanation

Caylee Davenport

Caylee Davenport

Expert

2022-07-24Added 14 answers

Step 1
1) 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 2
2) 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

Leila Jennings

Expert

2022-07-25Added 5 answers

Step 1
First 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's an easy integral.
Step 2
While 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

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