V= ∫ ∫ 4dydx + ∫ ∫ 4dydx

For the first set of integrals the outer limits are from 1 to 0. The inner limits are from X^2 to 0.

For the second set of integrals the outer limits are from 2 to 1. The inner limits are from (X-2)^2 to 0.

Sketch the limits of integration, and the shape of the prism, Change the order of limits and solve the volume of the prism.

I need help on changing the order of integration and sketching the prism. Please Help.

Question

V=  ∫ ∫ 4dydx + ∫ ∫ 4dydx
      
For the first set of integrals the outer limits are from 1 to 0. The inner limits are from X^2 to 0.

For the second set of integrals the outer limits are from 2 to 1. The inner limits are from (X-2)^2 to 0.

Sketch the limits of integration, and the shape of the prism, Change the order of limits and solve the volume of the prism.

I need help on changing the order of integration and sketching the prism. Please Help.

anonymous · Answer

$$Volume=\int\limits_{0}^{1}\int\limits_{0}^{x^2} 4dydx + \int\limits_{1}^{2}\int\limits_{0}^{(x-2)^2}4dydx$$

anonymous · Answer

I need the order to be as dxdy? and sketch the prism ? i guess the vol= pi*y^2

turingtest · Answer

the way the problem is given you are not doing a surface revolution, so we can supposed that 4 represents the height, so it's really just about changing the integration order
have you got a sketch yet?

anonymous · Answer

Oh yes the lengtth is 4cm sorry i missed that out!

anonymous · Answer

let me skecth it...

anonymous · Answer

|dw:1354460197419:dw|