Double Integral Help: Reversing Order & Finding Limits

[haris13]

∫u=3 and l=0 u= x and l= 0∫ (x2 + y2 )dydx

solve by reversing the order of integration. u and l means upper and lower limit. this is a double integral by the way. i don't understand how the limits are found when reversing the order and the idea of diagrams. please help me

 

[SammyS]

I take it you need to do the following integration by reversing the order of integration.

$$\int_0^3\int_0^x\,(x^2+y^2)\,dy\,dx$$

Sketch the region in the xy-plane.

Then consider how you might cover the same region with the order reversed.

 

[haris13]

I take it you need to do the following integration by reversing the order of integration.

$$\int_0^3\int_0^x\,(x^2+y^2)\,dy\,dx$$

Sketch the region in the xy-plane.

Then consider how you might cover the same region with the order reversed.

can you please help me with it. i have been trying to do it since last week. how do u change the limits with the order. that's my question. can you please explain for this particular question?

 

[Mark44]

Sketch the region in the xy-plane.

Then consider how you might cover the same region with the order reversed.

can you please help me with it. i have been trying to do it since last week. how do u change the limits with the order. that's my question. can you please explain for this particular question?

To repeat what SammyS said, sketch the region over which integration is being done. The limits of integration are x = 0 to x = 3, and y = 0 to y = x. What does this region in the plane look like?

 

[haris13]

thanks a lot..i got it :)