פורטל:מתמטיקה/נוסחה נבחרת/11

$\int _{a}^{b}f'(x)dx=f(b)-f(a)$

$\int _{\gamma }({\vec {\nabla }}f)\cdot {\vec {\mathrm {d} r}}=f(\gamma (b))-f(\gamma (a))$

$\oint _{\partial D}(P\,\mathrm {d} x+Q\,\mathrm {d} y)=\iint _{D}\left({\frac {\partial Q}{\partial x}}-{\frac {\partial P}{\partial y}}\right)\mathrm {d} x\,\mathrm {d} y$

$\iiint _{U}({\vec {\nabla }}\cdot {\vec {F}})\,\mathrm {d} V=\iint \limits _{\partial U}\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\;\;\;\subset \!\supset {\vec {F}}\cdot \mathrm {d} {\hat {n}}$,

$\oint _{\partial A}{\vec {F}}\cdot {\vec {\mathrm {d} l}}=\iint _{A}({\vec {\nabla }}\times {\vec {F}})\cdot \mathrm {d} {\hat {n}}$

$\int _{M}d\omega =\int _{\partial M}\omega$