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would have been lost from the tables, replacing missing data with
nulls.
There are three forms of the outer join, depending on which data is to
be kept.
LEFT OUTER JOIN - keep data from the left-hand table
RIGHT OUTER JOIN - keep data from the right-hand table
FULL OUTER JOIN - keep data from both tables OUTER JOIN
example 1 Figure : OUTER JOIN (left/right) OUTER JOIN example
2 Figure : OUTER JOIN (full)
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MATH 6A Evaluate the line integral
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2.Evaluate the line integral ∫C7xy4ds, where C is the right half of the
circle x2+y2=36
3.Evaluate the line integral ∫CF⋅dr,
where F(x,y,z)=−sinxi−2cosyj+4xzk and C is given by the vector
function r(t)=t5i−t4j+t3k , 0≤t≤1.
4.Sketch the vector field F⃗ (x,y)=xj⃗ , the line segment
from (1,4) to (7,4), and the line segment from (4,5) to(4,7).
(a) Calculate the line integral of the vector field F⃗ along the line
segment from (1,4) to (7,4).
(b) Calculate the line integral of the vector field F⃗ along the line
segment from (4,5) to (4,7).
5.Suppose F⃗ (x,y)=−ysin(x)i⃗ +cos(x)j⃗ .
(a) Find a vector parametric equation for the parabola y=x2 from the
origin to the point (4,16) using t as a parameter.
r⃗ (t)=
(b) Find the line integral of F⃗ along the parabola y=x2 from the
origin to (4,16).