Find the area enclosed by the curve x = t 2 − 2 t , y = t and the y-axis.

Question

Find the area enclosed by the curve   x  =      t    2    −  2  t  ,  y  =      t   and the y-axis.

francknightb0z · Accepted Answer

A  =      ∫          a              b        g  (  t  )      f    ′    (  t  )  d  t    x  =  f  (  t  )     a  n  d     y  =  g  (  t  )  Limit a and b, x=0  x  =      t    2    −  2  t        t    2    −  2  t  =  0    t  (  t  −  2  )  =  0    t  =  0  ,  2    A  r  e  a     A  =      ∫          0              2        (  2      t                  3        2              −  2      t                  1        2              )  d  t    =  [            4      ×      4              2              5    −            4      ×      2              2              3    ]  −  0  =            8              2              15      ≈  0.7542     s  q  u  a  r  e     u  n  i  t  s

Find the area enclosed by the curve x=t^2-2t, y=sqrt{t} and the y-axis.

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