Use the washers method and find k.
Can you solve for k?. Try Newton'e method if all else fails.
Let be a real number between 0 and . Let be the region in the first quadrant bounded by the x-axis, the line and the curve 0\le" alt="y=sin\:x\0\le" /> ). If the volume of the solid generated by revolving the region about the x-axis is , find the value of .
Thanks!
This one converges rather quickly, so Newton's method is a decent choice.
Let your initial guess be 1.5.
Let k=1.5:
Now, do it again with the answer we got above and we get 1.30900315524
Again: 1.30899693901
That's good enough.
Looks like x=1.309. There abouts.
There are numerous ways to go about it, but Newton's method can be handy to know.