\int_{C} x \sin y \; ds where C is the line segment form (10,3) to (4,6).


{eq}\int_{C} x \sin y \; ds {/eq} where {eq}C {/eq} is the line segment form {eq}(10,3) {/eq} to {eq}(4,6). {/eq}

Line Integrals:

Let a curve be defined by {eq}\mathbf r(t)=<x(t),y(t)>,\, a\leq t\leq b {/eq}. Recall that {eq}ds=||\mathbf r'(t)||\, dt {/eq} and the line integral of {eq}f(x,y) {/eq} over {eq}C {/eq} can be evaluated as

{eq}\int_C f(x,y)\, ds=\int_a^b f(x(t),y(t))||\mathbf r'(t)||\, dt. {/eq}

Answer and Explanation:

Recall that the vector from {eq}P(x_1,y_1) {/eq} to {eq}Q(x_2,y_2) {/eq} is {eq}\mathbf v=<x_2-x_1,y_2-y_1> {/eq}. The line segment will have...

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Learn more about this topic:

Line Integrals: How to Integrate Functions Over Paths

from GRE Math: Study Guide & Test Prep

Chapter 15 / Lesson 2

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