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anonymous

  • 5 years ago

If f prime (x) = sin(pi e^x/2) and f(0) = 1 then f(2) = ?

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  1. anonymous
    • 5 years ago
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    \[f \prime (x) = \sin(\pi e^x/2) and f(0)=1 then f(2)=?\]

  2. anonymous
    • 5 years ago
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    This is just like the other one. Knowing what integrals do.

  3. anonymous
    • 5 years ago
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    Integrals take the antiderivative of a function. Since f' is the first derivative of a function, taking the antiderivative of it gives the original function.

  4. anonymous
    • 5 years ago
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    Well considering theres a sin, pi, and e^x in there, its a bit intimidating! I'm not sure what to do with the pi or e

  5. anonymous
    • 5 years ago
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    Nothing, they're just constants. Since you're not actually having to calculate the integrals by hand, there's nothing more complicated about this than if you were given f'(x) = x Just remember that after you integrate, you add the constant C. That's needed to find the original f(x). Once you integrate, you have the equation f(0) = 1. Use it to make your f(x) by pluging in 1 for the resulting f(x) and 0 for your x value(s). Solving for C will let you have the full f(x) equation. After that, you just plug in 2 for your x values in f(2) to get your answer.

  6. anonymous
    • 5 years ago
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    Don't let the form of an integral intimidate you, it's all the same stuff.

  7. anonymous
    • 5 years ago
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    So would it just be \[\cos (\pi e^x/2)\] or do I need to do something else?

  8. anonymous
    • 5 years ago
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    forgot the "+ c" already

  9. anonymous
    • 5 years ago
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    Take the integral of it, not the derivative. It should return something different, as the derivative of cos(pi*e^x/2) is not sin(pi*e^x/2)

  10. anonymous
    • 5 years ago
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    Well then I'm confused.

  11. anonymous
    • 5 years ago
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    \[\int\limits_{?}^{?}sin(pi*e^x/2 dx\]

  12. anonymous
    • 5 years ago
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    I'm still lost

  13. anonymous
    • 5 years ago
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    I thought the integral would be \[- \cos(\pi e^x/2) + c\] but now I'm confused...

  14. anonymous
    • 5 years ago
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    Do you know chain rule?

  15. anonymous
    • 5 years ago
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    I've learned it before but I don't really remember it

  16. anonymous
    • 5 years ago
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    In this situation it's applied like so: For a trig function, you take the derivative of it as a whole(which is what you did) and multiply it by the derivative of the inside. If you took the derivative of your answer using chain rule, it wouldn't be the original equation, so it can't be correct.

  17. anonymous
    • 5 years ago
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    Try using u substitution on the integral before solving to simplify things.

  18. anonymous
    • 5 years ago
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    u substitution just makes things more complicated... Isn't there a quick, easy way to solve this?

  19. anonymous
    • 5 years ago
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    Not that I know of. It's actually not hard when you pick the right u. With the right u, it will end up in this form: http://en.wikipedia.org/wiki/Sine_integral#Sine_integral Then you just resubstitue and you're done with the hardest part. Then it's just a matter of finding f(2)

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