Integrating Vector Functions: Am I On the Right Track?

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SUMMARY

The discussion centers on computing the integral of the vector function r(t) = from π to 0. The user initially splits the integral into three components and arrives at the result of (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 be negated, indicating a potential misunderstanding of the limits of integration.

PREREQUISITES
  • Understanding of vector functions and their integrals
  • Familiarity with the concepts of definite integrals
  • Knowledge of trigonometric functions: cosine and sine
  • Basic calculus, specifically integration techniques
NEXT STEPS
  • Review the properties of definite integrals, particularly limits of integration
  • Study vector calculus, focusing on vector function integration
  • Explore the implications of reversing limits in integrals
  • Practice with similar vector function problems to reinforce understanding
USEFUL FOR

Students and professionals in mathematics, particularly those studying calculus and vector analysis, as well as educators looking to clarify integration concepts.

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
 
Physics news on Phys.org
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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