Evaluate the integral ∫ C F ⋅ d r , where C is the boundary of the region R and C is oriented so that the region is on the left when the boundary is traversed in the direction of its orientation. F x , y = e − x + 3 y i + x j ; C is the boundary of the region R inside the circle x 2 + y 2 = 16 and outside the circle x 2 − 2 x + y 2 = 3.
Evaluate the integral ∫ C F ⋅ d r , where C is the boundary of the region R and C is oriented so that the region is on the left when the boundary is traversed in the direction of its orientation. F x , y = e − x + 3 y i + x j ; C is the boundary of the region R inside the circle x 2 + y 2 = 16 and outside the circle x 2 − 2 x + y 2 = 3.
Evaluate the integral
∫
C
F
⋅
d
r
,
where C is the boundary of the region R and C is oriented so that the region is on the left when the boundary is traversed in the direction of its orientation.
F
x
,
y
=
e
−
x
+
3
y
i
+
x
j
;
C
is the boundary of the region R inside the circle
x
2
+
y
2
=
16
and outside the circle
x
2
−
2
x
+
y
2
=
3.
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.
find the zeros of the function algebraically:
f(x) = 9x2 - 3x - 2
Rylee's car is stuck in the mud. Roman and Shanice come along in a truck to help pull her out. They attach
one end of a tow strap to the front of the car and the other end to the truck's trailer hitch, and the truck
starts to pull. Meanwhile, Roman and Shanice get behind the car and push. The truck generates a
horizontal force of 377 lb on the car. Roman and Shanice are pushing at a slight upward angle and generate
a force of 119 lb on the car. These forces can be represented by vectors, as shown in the figure below. The
angle between these vectors is 20.2°. Find the resultant force (the vector sum), then give its magnitude
and its direction angle from the positive x-axis.
119 lb
20.2°
377 lb
University Calculus: Early Transcendentals (4th Edition)
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