calculus

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Let z = ∫(e^sin(t)dt) from x to y

a = x
b = y

I tried thinking about it like a chain rule but even then i'm a little unsure.

I know dz/dt = e^sin(t). Can you please point me in the right direction if i'm supposed to use the chain rule.

  • calculus -

    Don't know if you really meant
    ∫sin(t)e^t dt
    If that's the case, try differentiate using the chain rule,
    sin(t)e^t
    and
    cos(t)e^t

    You should be able to figure out the integral from the results.

    The original integral you posted does not seem to have an analytic solution. A series solution is (almost always) available but does not fit your bill.

  • calculus -

    uh no i meant what i typed which is e^(sin(t))

  • calculus -

    In that case, I fear there is no solution using elementary functions.

    who posed such a problem? It's solvable numerically, using a Taylor series, but not symbolically.

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