The popular fundamental theorem of calculus states that [tex]\int_{x_0}^{x_1} \frac{df}{dx}(x)dx = f(x_1)-f(x_0)[/tex] But I never see this theorem for a dobule integral... The FTC for a univariate function, y'=f'(x), computes the area between f'(x) and the x-axis, delimited by (x(adsbygoogle = window.adsbygoogle || []).push({}); _{0}, x_{1}), but given a bivariate function, z_{xy}=f_{xy}(x,y), you can want to compute the volume between a surface f_{xy}(x,y) and the xy-plane, delimited by ((x_{0}, x_{1}), (y_{0}, y_{1})). So, this volume is given by double integral [tex]\iint \limits_{y_0 x_0}^{y_1 x_1} \frac{\partial^2 f}{\partial y \partial x}(x,y)dxdy = f(x_1,y_1)-f(x_0,y_0)[/tex] Correct? If yes, what happens that anyone mentions this!?

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# Fundamental theorem of calculus for double integral

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