Scalar line integrals Evaluate the following line integrals along the curve C . 30. ∫ C ( 2 x − 3 y ) ds ; C is the line segment from (−1, 0) to (0, 1) followed by the line segment from (0, 1) to (1, 0).
Scalar line integrals Evaluate the following line integrals along the curve C . 30. ∫ C ( 2 x − 3 y ) ds ; C is the line segment from (−1, 0) to (0, 1) followed by the line segment from (0, 1) to (1, 0).
Scalar line integrals Evaluate the following line integrals along the curve C.
30.
∫
C
(
2
x
−
3
y
)
ds; C is the line segment from (−1, 0) to (0, 1) followed by the line segment from (0, 1) to (1, 0).
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.
Q1 Use the parametric equations to calculate the line integral .
in the graph
ху
ds over the path c which is given
y
(0 ,2p)
c2 a circular segment
C3 is line segment
C1 is line segment
(0,-2p)
Stokes' Theorem
(1.50) Given F = x²yi – yj. Find
(a) V x F
(b) Ss F- da over a rectangle bounded by the lines x = 0, x = b,
y = 0, and y = c.
(c) fc ▼ x F. dr around the rectangle of part (b).
Displacement d→1 is in the yz plane 62.8 o from the positive direction of the y axis, has a positive z component, and has a magnitude of 5.10 m. Displacement d→2 is in the xz plane 37.0 o from the positive direction of the x axis, has a positive z component, and has magnitude 0.900 m. What are (a) d→1⋅d→2 , (b) the x component of d→1×d→2 , (c) the y component of d→1×d→2 , (d) the z component of d→1×d→2 , and (e) the angle between d→1 and d→2 ?
Chapter 17 Solutions
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