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Fermat1
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How would I compute the following integral? Let t be in [0,1].
$\int_{0}^{t}|s-t|\,ds$
$\int_{0}^{t}|s-t|\,ds$
MHB Compute $\int_{0}^{t}|s-t|\,ds$: Step-by-Step Guide
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To compute the integral $\int_{0}^{t}|s-t|\,ds$ for $t$ in the interval [0,1], note that on this interval, $s$ is always less than $t$, making $|s-t| = -(s-t)$. This simplifies the integral to $-\int_{0}^{t} (t-s) \, ds$. Evaluating this gives $\left[ts - \frac{s^2}{2}\right]_{0}^{t}$, resulting in the expression $t^2/2$. Thus, the final result of the integral is $\frac{t^2}{2}$.
Hello!
I tried to calculate projections of curl using rotation of coordinate system but I encountered with following problem.
Given:
##rot_xA=\frac{\partial A_z}{\partial y}-\frac{\partial A_y}{\partial z}=0##
##rot_yA=\frac{\partial A_x}{\partial z}-\frac{\partial A_z}{\partial x}=1##
##rot_zA=\frac{\partial A_y}{\partial x}-\frac{\partial A_x}{\partial y}=0##
I rotated ##yz##-plane of this coordinate system by an angle ##45## degrees about ##x##-axis and used rotation matrix to...
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