Solids of Revolution: Integration (Two Curves) - VividMath.com

Here we are finding the volume of a function of two curves rotated about the y-axis using integration methods.

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[aguien]

Thank you very much, I didn't realize I had to differenciate y. I was doing with x and my aswer made no sense.

[glennrickelton]

At 2.09 minutes you took a "shortcut" which initially confused me. You took X squared = Y and put it straight into the X squared - X squared equation. Normally, I would have taken X squared = Y and removed the square on X by taking the square root of both sides so X = ✓Y. Then putting this into the equation and squaring ✓Y = Y. I normally use large R squared - small R squared for this problem (Washer Method) but using X squared - X squared saved a bit of time in this instance

[glennrickelton]

At 2.09 mins you took a "shortcut" which confused me at first as you left X squared = Y and put it into the equation. I would have normally made X squared = Y = X squared = ✓ Y. Then the ✓ Y would cancel to Y when being squared in the formula of X squared -X squared. I normally use R squared - R squared but as you used Xs I see it can be plugged straight in