Please help with Volumes of Solids: Let f(x)= cos(x) and g(x)= 1-(x^2/ 2)...

[AmbR]

Let f(x)= cos(x) and g(x)= 1-(x^2/ 2).
Let D be the region bounded by the graph of f(x) and the x-axis between x= -π/2 and x= π/2 and let A be the region bounded by the graph g(x) and the x-axis.

a) Use the Shells Method to find the volume of the solids generated by rotating D and A around the y-axis.

 

[Deleted member 4993]

Let f(x)= cos(x) and g(x)= 1-(x^2/ 2).
Let D be the region bounded by the graph of f(x) and the x-axis between x= -π/2 and x= π/2 and let A be the region bounded by the graph g(x) and the x-axis.

a) Use the Shells Method to find the volume of the solids generated by rotating D and A around the y-axis.

What are your thoughts?

Please share your work with us ...even if you know it is wrong.

If you are stuck at the beginning tell us and we'll start with the definitions.

You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

http://www.freemathhelp.com/forum/announcement.php?f=33

 

[AmbR]

What are your thoughts?

Please share your work with us ...even if you know it is wrong.

If you are stuck at the beginning tell us and we'll start with the definitions.

You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

http://www.freemathhelp.com/forum/announcement.php?f=33

I am stuck on setting up the 2 integrals.
So far for region D I have:

. . . . .\(\displaystyle \displaystyle 2\pi\, \int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}\, x\, \left(1\, -\, \dfrac{x^2}{2}\, +\, \cos(x)\right)\, dx\)

And I am totally lost on how to begin to set you the second integral.

 

[stapel]

I am stuck on setting up the 2 integrals.
So far for region D I have:

. . . . .\(\displaystyle \displaystyle 2\pi\, \int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}\, x\, \left(1\, -\, \dfrac{x^2}{2}\, +\, \cos(x)\right)\, dx\)

And I am totally lost on how to begin to set you the second integral.

You seem to have combined both functions into one integral. Doesn't the exercise specify that the one integral uses only f(x), and the other integral uses only g(x)?