Calculate the work done by a force in moving a particle counter clockwise along the circle x2+y2=4 from the point (2, 0) to the point (0, -2).
To calculate the work done by the force \(\vec{F} = (x+y) \hat{i} + xy \hat{j}\) along the given circular path, we use the line integral: \[ W = \int_C \vec{F} \cdot d\vec{r} \] ### Step 1: Parameterizing the Path The given path is the circle: \[ x^2 + y^2 = 4 \] We use the parametric equations for a circle of radius 2: \[ x = 2\cos t, \quad y = 2\sin t, \quad t __________ __________ ________ _________ ______ ______ _______.
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random variable X has the following probability distribution:
Determine the value of the constant k and E(X).
सदिश फलन का डाइवर्जेन्स परिकलित करें।
का मान प्राप्त करें।
ख) सिद्ध करें कि किसी भी अदिश क्षेत्र के लिए:
होता है।
Obtain a unit tangent vector to any point on the curve defined by the parameteric equations:
x = sin 3t; y = 2 cos 3t;z = 4t.
b) Obtain the directional derivative for a scalar field at the point (1,-2,-1) in the direction
.
Using the divergence theorem evaluate where
and S is the surface of the cube defined by
बल द्वारा एक कण को वृत्त x² + y² = 4 के अनुदिश वामावर्त दिशा में बिंदू (2,0) से बिंदु (0,-2) तक ले जाने में किया गया कार्य परिकलित करें।
Evaluate .
b) Show that for any scalar field :
.