Green’s Theorem for line integrals Use either form of Green’s Theorem to evaluate the following line integrals. 31. ∮ C ( x 3 + x y ) d y + ( 2 y 2 − 2 x 2 y ) d x ; C is the square with vertices (±1, ±1) with counterclockwise orientation.
Green’s Theorem for line integrals Use either form of Green’s Theorem to evaluate the following line integrals. 31. ∮ C ( x 3 + x y ) d y + ( 2 y 2 − 2 x 2 y ) d x ; C is the square with vertices (±1, ±1) with counterclockwise orientation.
Solution Summary: The author evaluates the value of the line integral displaystyleundersetCoint.
Green’s Theorem for line integralsUse either form of Green’s Theorem to evaluate the following line integrals.
31.
∮
C
(
x
3
+
x
y
)
d
y
+
(
2
y
2
−
2
x
2
y
)
d
x
;
C is the square with vertices (±1, ±1) with counterclockwise orientation.
With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.
Trolley of the overhead crane moves along the bridge rail. The trolley position is
measured from the center of the bridge rail (x = 0) is given by x(t) = 0.5t^3-6t^2+19.5t-14 : 0 <= t <= 3 min. The
trolley moves from point A to B in the forward direction, B to C in the reverse direction and C to D again in the
forward direction.
CONTROL PANEL
END TRUCK-
RUNWAY BEAM-
BRIDGE RAIL
HOIST
-TROLLEY
TROLLEY BUMPER
TROLLEY DRIVE
LPENDANT TRACK
-TROLLEY CONDUCTOR
TRACK
WIRE ROPE
-HOOK BLOCK
-BRIDGE DRIVE
-END TRUCK BUMPER
-RUNWAY RAIL
TROLLEY END STOP
-CONDUCTOR BAR
PENDANT FESTOONING
TROLLEY FESTOONING
PENDANT CABLE
PENDANT
x(t)=0.5t^3-6t^2+19.5t-14
v(t)=1.5t^2-12t+19.5
a(t)=(dv(t))/dt=3t-12
Fig. T2.2: The overhead crane
Total masses of the trolley, hook block, and the load attached to the hook block are 110 kg, 20
kg, and 150 kg. Damping coefficient, D, is 40 kg/s.
What is the total amount of energy required from the trolley motor to move the system
[Hint: Use Newton's 2nd law to obtain the…
CONTROL PANEL-
BRIDGE RAIL
HOIST
-TROLLEY
TROLLEY BUMPER
-BRIDGE DRIVE
END TRUCK-
RUNWAY BEAM-
END TRUCK BUMPER
-RUNWAY RAIL
TROLLEY DRIVE
TROLLEY END STOP
-CONDUCTOR BAR
LPENDANT TRACK
TROLLEY CONDUCTOR
TRACK
-WIRE ROPE
PENDANT FESTOONING
TROLLEY FESTOONING
-PENDANT CABLE
-HOOK BLOCK
PENDANT
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.
MFCS unit-1 || Part:1 || JNTU || Well formed formula || propositional calculus || truth tables; Author: Learn with Smily;https://www.youtube.com/watch?v=XV15Q4mCcHc;License: Standard YouTube License, CC-BY