Complex integration: $ \int_ {c} \frac {e^ {z}} {z (z-3)} dz ...
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What does $\\int_C \\mathbf{r} \\cdot d\\mathbf{r}$ mean?
2023年7月1日 · This is precisely what is happening here: $\int_C \mathbf r \cdot d \mathbf r$ is just the line integral $\int_C \mathbf F(\mathbf r) \cdot d \mathbf r$ of the vector field $\mathbf F(\mathbf r) = \mathbf r$, i.e. the vector field that associates to the point at the position $\mathbf r$ the position vector $\mathbf r$ itself (often referred to ...
Show that $cl(A) = int(A^c)^c$ - Mathematics Stack Exchange
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calculus - Evaluate the line integral $\int_C \mathbf F \cdot ...
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Integral of $\\int_C \\frac{1}{z^2-z} dz$ where $C$ is a circle of ...
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integration - Evaluating $\int_C\frac {z+1} {z^2-2z}dz$, where $C
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Interpreting the integral identity $\int c f (x) \,dx = c \int f (x ...
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calculus - Prove that $E (X) = \int_ {0}^ {\infty} P (X>x)\,dx = \int ...
2016年3月10日 · $$\mathsf P(X> x) = \int_x^\infty f_X(y)\operatorname d y$$ Then taking the definite integral (if we can): $$\int_0^\infty \mathsf P(X> x)\operatorname d x = \int_0^\infty \int_x^\infty f_X(y)\operatorname d y\operatorname d x$$ To swap the order of integration we use Tonelli's Theorem, since a probability density is strictly non-negative.
How to solve $\\int_C Im(z) dz$ where $C$ is the unit circle
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find $\\int_C \\left\\vert z \\right\\vert dz$ where $C$ is the left ...
Evaluating $\int_C \frac{dz}{(e^{2 \pi z}+1)^2}$ on the upper half-circle 3 Why am I getting two different answers when the countour integral is performed in two different ways?