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is there an exact way to calculate the volume of a shape where one shape is revolved around a parabolic curve (obviously with limits).

i dont know much about this stuff but im pretty sure u need to integrate it.

the shape revolved is a rectangle (vertical) with a triangle connected at the vertices

for a birds eye view there are 3 (given) parabolic curves. the area between the top and middle curves represent the area on the top of the shape. the area between the middle and bottom represent the area on the bottom of the shape.

i have to find a way to calculate it.

i have no idea.

i tried integrating the curves to find the areas for the top and base and averaging them and multiplying by the height. (basically trapeoid rule sort of)

but this is only an approximation!!!!!

CAN ANYONE GIVE ME AN ACCURATE WAY OR A BETTER APPROXIMATION!!!!

help!!!!

need help urgently

i dont know much about this stuff but im pretty sure u need to integrate it.

the shape revolved is a rectangle (vertical) with a triangle connected at the vertices

for a birds eye view there are 3 (given) parabolic curves. the area between the top and middle curves represent the area on the top of the shape. the area between the middle and bottom represent the area on the bottom of the shape.

i have to find a way to calculate it.

i have no idea.

i tried integrating the curves to find the areas for the top and base and averaging them and multiplying by the height. (basically trapeoid rule sort of)

but this is only an approximation!!!!!

CAN ANYONE GIVE ME AN ACCURATE WAY OR A BETTER APPROXIMATION!!!!

help!!!!

need help urgently