Integrating Vector Functions: Am I On the Right Track?

AI Thread Summary
The discussion centers on computing the integral of the vector function r(t) = <e^t, cos(t), sin(t)> from π to 0. The user claims to have split the integral into three parts, resulting in the expression (e^(π) - 1)i + (0)j + (2)k. However, another participant points out that if the integral is indeed from π to 0, the results should include a negative sign, suggesting a potential misunderstanding in the limits of integration. Clarification is needed regarding the direction of integration to confirm the accuracy of the calculations. The conversation emphasizes the importance of correctly applying integration limits in vector calculus.
crazynut52
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Can someone check my work and see if I am on the right track please?

the problem is:

if r(t) = <e^t, cost, sint> compute integral from pi to 0 of r(t)dt

so I split it into three integrals, and ended up with (e^(pi) - 1)i + (0)j + (2)k

does this sound right?

Thanks
 
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Yup.
bladibladibla
 
from pi to 0 or 0 to pi?? If it is from pi to 0 as you said, then all of your answers should have a negative in from of them...unless you meant 0 to pi
 
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