Use a graph of the vector field F and the curve C to guess whether the line integral of F over C is positive, negative or zero. Then evaluate the line integral. F ( x , y ) = x x 2 + y 2 i + y x 2 + y 2 j , C is the parabola y = 1 + x 2 from ( − 1 , 2 ) to ( 1 , 2 )
Use a graph of the vector field F and the curve C to guess whether the line integral of F over C is positive, negative or zero. Then evaluate the line integral. F ( x , y ) = x x 2 + y 2 i + y x 2 + y 2 j , C is the parabola y = 1 + x 2 from ( − 1 , 2 ) to ( 1 , 2 )
Solution Summary: The author explains that the line integral of F over C is positive, negative, or zero by using a graph of the vector field.
Use a graph of the vector field F and the curve C to guess whether the line integral of F over C is positive, negative or zero. Then evaluate the line integral.
F
(
x
,
y
)
=
x
x
2
+
y
2
i
+
y
x
2
+
y
2
j
,
C is the parabola
y
=
1
+
x
2
from
(
−
1
,
2
)
to
(
1
,
2
)
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
Use the properties of logarithms, given that In(2) = 0.6931 and In(3) = 1.0986, to approximate the logarithm. Use a calculator to confirm your approximations. (Round your answers to four decimal places.)
(a) In(0.75)
(b) In(24)
(c) In(18)
1
(d) In
≈
2
72
Find the indefinite integral. (Remember the constant of integration.)
√tan(8x)
tan(8x) sec²(8x) dx
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