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

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Accepted Answer

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

Answer

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

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

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