Evaluate a Definite Integral to find Work

[bmb2009]

Homework Statement

Evaluate: from x=0 to x=1 and y=0 to y=1

∫(y^2 + 2xy(dy/dx))dx and carry the integration out over x

Homework Equations

The Attempt at a Solution

I know how to calculate double integrals with multiple variables but the (dy/dx) throws me off and it says to carry out the integration over x which to means that it isn't a double integral at all? Can some one explain to me how to deal with this integral? Thanks!

 

[pasmith]

Homework Statement

Evaluate: from x=0 to x=1 and y=0 to y=1

∫(y^2 + 2xy(dy/dx))dx and carry the integration out over x

Homework Equations

The Attempt at a Solution

I know how to calculate double integrals with multiple variables but the (dy/dx) throws me off and it says to carry out the integration over x which to means that it isn't a double integral at all? Can some one explain to me how to deal with this integral? Thanks!

The question is somewhat unclear, but I think it is asking you to evaluate the given line integral over the line $y = x$ from $(0,0)$ to $(1,1)$. So substitute $y = x$ and $dy/dx = 1$ in the integrand and integrate with respect to $x$.

 

[haruspex]

Homework Statement

Evaluate: from x=0 to x=1 and y=0 to y=1

∫(y^2 + 2xy(dy/dx))dx and carry the integration out over x

The integrand has a rather interesting property. It can be written in the form d(f(x,y)). So the answer will be independent of path.