Now, there is still no F but we know that we want so in the first case the integ

Question

Now, there is still no F but we know that we want

so in the first case the integral could then be written as

then by using a u-sub where u=2t you get

Now, I didn't show the work because it's very similar, but if you follow the same steps with the second parameterization you end up getting the same integral of

Thus they are the same.

Consider the parameterizations r_1 (t) = (2t, 2t), 0 lessthanorequalto t lessthanorequalto 1/2 and r_2 (t) = (t^2 - 1/3, t^2 - 1/3), 1 lessthanorequalto t lessthanorequalto 2 of the oriented line segment from (0, 0) to (1, 1). Calculate integral_C F middot dr for each of the two parameterizations. integral_C F middot dr integral_C F(r(t) middot r'(t) integral_0^1 middot dt integral_0^1/2 middot dt = integral_0^1/2 2P(2t, 2t) + 2Q(2t, 2t)dt integral_0^1 P(u, u) + Q(u, u)du integral_0^1 P(u, u) + Q(u, u)du

Explanation / Answer

yeah that is the way to do it

for ssecond case your u = (t^2 -1 )/3

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