How to find the volume under a paraboloid and above a disk using double integration

[@thevocatiousunspeakables709]

Hey, nice video! Its very comprehensible compared to my calculus 3 experience lol. From what I understand, the integral ends at theta = pi because the cylinder is not at the center of the coordinate plane. Is this the correct way of interpreting this?

[@JohnsMathsBook]

Try using 90 to -90, evaluate the integral and let me know what answer you get.Shouldn’t take long

[@thevocatiousunspeakables709]

If you use -pi/2 to pi/2, you would get an answer of 0 which is clearly not correct. So, 0 to pi accounts for the asymmetrical cut into the cylinder, right?

[@JohnsMathsBook]

Did you verify this? If not, have a go. Remember when evaluating the limits of the integral it’s the upper limit minus the lower limit and the lower limit in this case is negative if you use -pi/2. Let me know what answer you get.

[@monkey_b00ts63]

Why does the interval of theta is from 0 to pi. Isnt it from -pi/2 to pi/2?

[@JohnsMathsBook]

Just for fun evaluate the integral between pi/2 and -pi/2 and let me know what answer you get.

[@monkey_b00ts63]

@@JohnsMathsBook Thank you so much for the video. I just want to let you know that tomorrow i have calculus final exam and it worth 30% of my grade. Have a great day sir

[@JohnsMathsBook]

Thanks and good luck with your exam. Glad the video helped.