Calculus 2

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The question is:
Evaluate the improper integral for a>0.

The integral is:
the integral from 0 to infinity, of e^(-y/a)dy

Can anyone help me solve this? When I try I get 'a', which apparently is incorrect. Thank you!

  • Calculus 2 -

    ∫e^(-y/a) dy
    = -a(e^(-y/a) from 0 to ∞
    = -a/e^(y/a) from 0 to ∞

    as y -->∞
    a/e^(y/a) ---> 0

    so the integral from above
    = 0 - (a/e^0) )
    = 0 - a/1
    = -a

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