Evaluate $\int\int(yx^2-2xy^2)dydx$: Get Help Here!

[der.physika]

$$\int\int(yx^2-2xy^2)dydx$$

limits for the first are 0 $$\longrightarrow$$ 3

limits for the second are -2 $$\longrightarrow$$ 0

solve! help

 

[tiny-tim]

Hi der.physika!

(type "\int_0^3\int_{-2}^0" )

Just split it into two integrals, ∫∫ yx² dydx and ∫∫ 2xy² dydx …

what do you get? ​

 

[der.physika]

Hi der.physika!

(type "\int_0^3\int_{-2}^0" )

Just split it into two integrals, ∫∫ yx² dydx and ∫∫ 2xy² dydx …

what do you get? ​

Okay so I took your advice and split the integral and I got 6, is that the correct answer?

 

[tiny-tim]

erm … i can't check your answer without seeing your calculations, can I?

 

[der.physika]

erm … i can't check your answer without seeing your calculations, can I?

$$\int\int(yx^2dydx)-2\int\int(xy^2dydx)$$

$$\int[\frac{1}{2}y^2x^2]=\int(-2x^2dx)=[\frac{-2}{3}x^3]=\frac{-54}{3}$$

$$-2\int\int(xy^2dydx)=-2\int[\frac{1}{3}y^3x]=-2(-12)=24=\frac{72}{3}$$

$$=\frac{72}{3}+\frac{-54}{3}=\frac{18}{3}=6$$

is this okay?

 

[tiny-tim]

Sorry, I'm totally confused.

Where are your half-way integrals, ie after just one integration?

(and btw, which integral is going from 0 to 3, ∫ dx or ∫ dy?)

 

[der.physika]

Sorry, I'm totally confused.

Where are your half-way integrals, ie after just one integration?

(and btw, which integral is going from 0 to 3, ∫ dx or ∫ dy?)

How do you put in limits on the integral? I don't know how to put the code into LaTex

 

[tiny-tim]

I showed you above … type "\int_0^3" and "\int_{-2}^0"

(you need {} if the limit has more than one character, eg -2)