Where on the axis is the centre?
I really need help with the following question, i dont even know where to start:
Use triple integration in Cylindrical coordinates to find the volume of the region that lies inside both the sphere of radius 2 centered at the origin and the cylinder of radius 1 with the zaxis as its centre.
Thanks soo much
Assuming 'centre' meant 'axis', and doing just the top hemisphere, we have z going from 0 (where it 'starts', on the (x,y) plane) up to (where it hits the hemisphere). And we have r going from 0 at the centre (z axis), up to 1 where it hits the cylinder. And theta is going a full turn. So...
Just in case a picture helps to follow through from the inside out, we can start bottom left here, integrating r with respect to z...
... where (key in spoiler) ...
Spoiler:
Which leaves a couple of blanks to fill. Hope this helps.
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