I'm integrating some parametric functions and I came across this one and it's confusing since it fundamentally doesn't make sense x = t 5 − 4 t 3 y = t 2 How would I approach this problem, if I were to, say integrate from t = − 3 to t = 3?

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I&#039;m integrating some parametric functions and I came across this one and it&#039;s confusing since it fundamentally doesn&#039;t make sense  x  =      t    5    −  4      t    3    y  =      t    2  How would I approach this problem, if I were to, say integrate from   t  =  −  3 to   t  =  3?

Bria Berg · Accepted Answer

Step 1Your path must be closed in order to form an area.   [  −  3  ,  3  ] will not do.   [  −  2  ,  2  ] will work.That is:   x  (  −  2  )  =  x  (  2  ) and   y  (  −  2  )  =  y  (  2  )Area:   ∫  y     d  x  =  −  ∫  x     d  yYou can solve either one... but just do demonstrate that the two are equal, I will do both.      ∫          −      2        2        t    2    (  5      t    4    −  12      t    2    )     d  t  =  −      ∫          −      2        2    (      t    5    −  4      t    3    )  (  2  t  )     d  t        ∫          −      2        2    5      t    6    −  12      t    4       d  t  =  −      ∫          −      2        2    2      t    6    −  8      t    4       d  t    2  (      5    7        2    7    −      12    5        2    5    )  =  −  2  (      2    7        2    7    −      8    5        2    5    )    2  (      512    35    )  =  −  2  (  −      512    35    )

I'm integrating some parametric functions and I came across this one and it's confusing since it fun

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