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A gate of a reservoir is hinged at a point and it is prevented from opening by the force in the spring.
The gate is 3m high and 1m wide. The level of water is 2m above the top of the gate.
Determine the force in the spring if the gate is just about to open

Find the area bounded by the curves x=y²,x+y-2=0


Using Green's theorem,evaluate ∮c(x+y)dx+ x²dy, C is the triangle

with vertices at (0,0). (2,0) and (2, 4), taken in that order.


Find the work done by a force F= -xyi+y²j + zk in moving a particle over the circular path x² + y² = 4, z = 0 from (2,0,0) to (0,2,0)


Find the constants a, b, c if the vector F = (2x+3y+az)i + (bx+2y+3z)j + (2x+cy+3z)k is conservative.


By Changing the order of Integration and evaluate ∫0^{a}∫0^{√a^{2}-y^{2}}(x^{2}+y^{2})dxdy `
Evaluate the integral ∫0^{2a}∫0^{x}∫y^{x} xyzdzdydx
Show that curl(curl→{v})=grad(div→{v})-V^{2}→{v},→{v} is any vector and if isolenoidal, then find curl (curl →{v)?

Evaluate ∫y=0^{1}∫x=y^{√2-y^{2}}y/√x^{2}+y^{2}dxdy ,by clange the order of integration.


Solve ∫y=0 ^ 1 ∫x=y^ 2 ^ 1∫z=0 ^ 1-x x dzdxdy ?derive the problem with step by step?


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