Select all the triangles that would have an area of 16 square inches. Answer Choices A triangle with a base length of 8 in. and
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F(x) = (x + 1)(x - 2)
f(x) = x(x - 2) + 1(x - 2)
f(x) = x(x) - x(2) + 1(x) - 1(2)
f(x) = x² - 2x + x - 2
f(x) = x² - x - 2
f(x) = x(x - 2) + 1(x - 2)
f(x) = x(x) - x(2) + 1(x) - 1(2)
f(x) = x² - 2x + x - 2
f(x) = x² - x - 2
is conservative if there is a scalar function such that
. This would require
(or perhaps the last partial derivative should be 4 to match up with the integral?)
From these equations we find
so is indeed conservative, and the gradient theorem (a.k.a. fundamental theorem of calculus for line integrals) applies. The value of the line integral depends only the endpoints: