Problem

Evaluate $\int_{C}(x+y) d s, C: x=2 t, y=-2 t+2$, for $-1 \leq t \leq 1$

Solution

Step 1 :Given the line integral \(\int_{C}(x+y) d s\), where the curve C is parameterized by \(x=2 t\) and \(y=-2 t+2\) for \(-1 \leq t \leq 1\)

Step 2 :Substitute the parameterizations of x and y into the integral to get \(\int_{C}(2t - 2t + 2) d s\)

Step 3 :Simplify the integral to \(\int_{C}2 ds\)

Step 4 :Calculate the integral of ds from -1 to 1 to get 4

Step 5 :Thus, the value of the line integral over the curve C is \(\boxed{4}\)

From Solvely APP
Source: https://solvelyapp.com/problems/8967/

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