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Math Help - Integrals?

  1. #1
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    Integrals?

    If you know f(x) is continuous, even and: f(t)dt=2 on the integral 0 to 2, f(t)dt=-1 on the integral 1 to 2, and f(t)dt=7 on the integral 2 to 4:


    What is f(t)dt on the integral -1 to 2

    What is f(t-1)dt on the integral 1 to 2


    and what is the average value of f(x) on the interval [-4,4]

    Thank you so much!
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  2. #2
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    Re: Integrals?

    Hey irock3337.

    Hint: Remember that Integral [a,b] + Integral [b,c] = Integral[a,c] where a < b < c. Try using this and re-arranging to get the answers to these questions.
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  3. #3
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    Re: Integrals?

    Since it's an even function, you also have \int_a^bf(t)\,dt = \int_{-b}^{-a}f(t)\,dt where a,b > 0. You'll need that.

    If you're having trouble getting started, try to find \int_0^1f(t)\,dt using the equation chiro gave you.

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