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Math Help - Line integral

  1. #1
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    Line integral

    Calculate the line integral on the s along the curve C

    \int_C \frac{x}{1+y^2}ds
    C: x = 1+2t; y = t; (0 \leq t \leq 1)
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  2. #2
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    Quote Originally Posted by Apprentice123 View Post
    Calculate the line integral on the s along the curve C

    \int_C \frac{x}{1+y^2}ds
    C: x = 1+2t; y = t; (0 \leq t \leq 1)

    Remember

    ds=\sqrt{\left( \frac{dx}{dt} \right)^2 +\left( \frac{dy}{dt} \right)^2 }dt

    \int_{0}^{1}\frac{1+2t}{1+t^2}\sqrt{(2)^2+1^2}dt

    You should be able to finish from here
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  3. #3
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    Thank you.

    Please check if these are correct
    1)
    F(x,y) = x^2yi +4j
    C: r(t) = e^t i + e^{-t} j; (0 \leq t \leq 1)

    My solution:

    \int_0^1 (e^t,4).(e^t,-e^{-t})dt
    = \frac{9}{2}e+\frac{7}{2}

    2)
    F(x,y,z) = zi+xj+yk
    C: r(t) = senti + 3sentj + sen(t)^2k; (0 \leq t \leq \frac{ \pi}{2})
    My Solution:

    \int_0^{\frac{ \pi}{2}} (sen(t)^2, sent, 3sent).(cost, 3cost, 2sentcost)dt
    = \frac{23}{6}


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