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. Let C be a smooth curve with arc length L, and suppose that f(x, y) = P(x, y)i +Q(x, y)j is a vector field such that $|| f|(x,y) || \leq M $ for all (x,y) on C. Show that $\left\vert\displaystyle\int_C f \cdot dr \right\vert \leq ML $
Hint: Recall that $\left\vert\displaystyle\int_a^b g(x) dx\right\vert \leq \displaystyle\int_a^b |g(x) | dx $ for Riemann Integrals.
Now, how to prove this corollary using this hint?
Hint: Recall that $\left\vert\displaystyle\int_a^b g(x) dx\right\vert \leq \displaystyle\int_a^b |g(x) | dx $ for Riemann Integrals.
Now, how to prove this corollary using this hint?