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    Definite Integral

    integral from -1 to 1 of (x^99)*cosh(x)dx

    apparently, the answer is obtained very easily with minimal work...i don't see it....
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    Re: Definite Integral

    Quote Originally Posted by softstyll View Post
    integral from -1 to 1 of (x^99)*cosh(x)dx

    apparently, the answer is obtained very easily with minimal work...i don't see it....
    \displaystyle f(x) &= x^{99}\cosh{x} \\ f(-x) &= (-x)^{99}\cosh{(-x)} \\ f(-x) &= -x^{99}\cosh{x} \\ f(-x) &= -f(x)

    This is an odd function. What do you know about definite integrals of odd functions?
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    Re: Definite Integral

    Quote Originally Posted by Prove It View Post
    \displaystyle f(x) &= x^{99}\cosh{x} \\ f(-x) &= (-x)^{99}\cosh{(-x)} \\ f(-x) &= -x^{99}\cosh{x} \\ f(-x) &= -f(x)

    This is an odd function. What do you know about definite integrals of odd functions?
    Thank you. I understand that the integral of an odd function from -a to a is a constant. But I don't understand how u can just say that f(x) is the integrand.
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    Re: Definite Integral

    Quote Originally Posted by softstyll View Post
    Thank you. I understand that the integral of an odd function from -a to a is a constant. But I don't understand how u can just say that f(x) is the integrand.
    Yes it is a constant, in fact, it's 0.

    Maybe the reason I know that f(x) is the integrand is because you told me what the integrand was... ><
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    Re: Definite Integral

    Quote Originally Posted by softstyll View Post
    Thank you. I understand that the integral of an odd function from -a to a is a constant. But I don't understand how u can just say that f(x) is the integrand.
    Do you understand \int_{ - 99}^{99} {(x^3  + \sin ^{999} (x))dx}  = 0 and WHY?
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