Given the polynomial 21x 4 + 3y - 6x 2 + 34 What polynomial must be added to it to obtain a first degree polynomial?
1 answer:
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a. Parameterize by
with .
b/c. The line integral of over
is
d. Notice that we can write the line integral as
By Green's theorem, the line integral is equivalent to
where is the triangle bounded by
, and this integral is simply twice the area of
.
is a right triangle with legs 2 and 5, so its area is 5 and the integral's value is 10.