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Math Help - Line integral

  1. #1
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    Line integral

    1)
    \int_C 3x^2yzds
    C: x=t, y=t^2, z=\frac{2}{3}t^3 ; (0 \leq t \leq 1)

    My solution

    \int_0^1 2t^7 \sqrt{1+4t^2+4t^4}dt = \frac{13}{20}


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

    My solution:

    \int_0^{\frac{ \pi}{2}} (-sint - cos^2t)dt


    Is correct ?
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  2. #2
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    Both are correct. A little trick for the first integral is to use that 4t^4 +4t^2+1=(2t^2+1)^2
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  3. #3
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    Thank you
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