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I don't know how to apply Leibniz's rule for this integrand. I believe there is a substitution to allow me to express this integral differently, but the partial being a function of what we're integrating by is confusing me.

[itex]\int^{b}_{a} \frac{\partial f(x,y)}{\partial y(x)} dx[/itex]

Knowns are that [itex][a,b][/itex] is a subset of the domain of [itex]x[/itex] and that [itex]y[/itex] is a function of [itex]x[/itex].

Can someone please suggest something to get me started, or ask me a question that may get my brain going in the right direction?

I attempted working with [itex]\int^{b}_{a} \frac{\partial f(x,y)}{\partial x} \frac{dx}{dy}dx[/itex] by expanding the partial according to the chain rule, but I didn't think it helped me.

Edit: I didn't think the above would help because what exactly does [itex][f(b,y) - f(a,y)]\frac{dx}{dy}[/itex] mean? I don't know how to interpret the factor [itex]\frac{dx}{dy}[/itex].

[itex]\int^{b}_{a} \frac{\partial f(x,y)}{\partial y(x)} dx[/itex]

Knowns are that [itex][a,b][/itex] is a subset of the domain of [itex]x[/itex] and that [itex]y[/itex] is a function of [itex]x[/itex].

Can someone please suggest something to get me started, or ask me a question that may get my brain going in the right direction?

I attempted working with [itex]\int^{b}_{a} \frac{\partial f(x,y)}{\partial x} \frac{dx}{dy}dx[/itex] by expanding the partial according to the chain rule, but I didn't think it helped me.

Edit: I didn't think the above would help because what exactly does [itex][f(b,y) - f(a,y)]\frac{dx}{dy}[/itex] mean? I don't know how to interpret the factor [itex]\frac{dx}{dy}[/itex].

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