integration

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sqrt2 times e^t times t^(1/2) dt bounded between 0 and 1.

i tried integration by parts.. but it keeps repeating.. please help. thank you!

  • Math -

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  • integration -

    Let's leave out the constant sqrt2 and do the rest. The constant can be multiplied back later.
    I will use S to represent the integral sign.

    Let u = e^t ; du = e^t dt
    Let v = t^(1/2) ; dv = (1/2) t^(-1/2)
    S u dv = e^t*t^(1/2) - S t^(1/2) e^t dt
    = e^t*t^(1/2) - S u dv
    Therefore
    2 S u dv = e^t*t^(1/2)
    S u dv = (1/2) e^t*t^(1/2)
    Multiply that by sqrt2 for the integral you were asked for.

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