Verla
MathCalculus

Evaluate the Following Line Integral Along the Curve C

Explore this calculus question in math. Members can read the complete answer, explanation, and references.

Question

Evaluate the following line integral along the curve CC:

∫C(x−y) ds,C:r(t)=4t i+3t j,0≤t≤2.\int_C(x-y)\,ds, \qquad C:\mathbf r(t)=4t\,\mathbf i+3t\,\mathbf j, \quad 0\le t\le2.

This question has been answered.

Explore the full answer and supporting references to better understand this question.

Verla BasicBest value

$19.99/month

  • Everything in Study Pass
  • Assignments with writing output
  • AI detection and humanizer
  • Basic quotas across every tool
Study Pass

$0.99/month

  • Entire question library
  • Knowledge guides and sources
  • Detailed answers and explanations
  • No AI tools or quotas

Evidence boundary

The integrand, parameterization and parameter interval are taken from the cited OpenStax exercise. The result follows from the scalar line-integral definition and an exact calculation. Although the exercise group permits a computer algebra system, the displayed derivation does not depend on one.