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Math Help - Intergrals

  1. #1
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    Intergrals

    Can someone please hlep me/ show me how to do this problem!! thannks
    1. Let .
    Find ????
    and ???
    Note: You should use the first part to do the second part!

    2. Use the First Fundamental Theorem of Calculus to find the derivative of
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  2. #2
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    Quote Originally Posted by Kayla_N View Post
    Can someone please hlep me/ show me how to do this problem!! thannks
    1. Let .
    Find ????
    and ???
    Note: You should use the first part to do the second part!

    2. Use the First Fundamental Theorem of Calculus to find the derivative of
    properties of definite integrals

    1. \int_6^{15} f(x) \, dx = \int_6^9 f(x) \, dx + \int_9^{12} f(x) \, dx + \int_{12}^{15} f(x) \, dx

    solve for \int_9^{12} f(x) \, dx ... you were given the values for all the other definite integrals.

    \int_{12}^9 7f(x) - 7 \, dx =

    7\int_{12}^9 f(x) - 1 \, dx = -7\int_9^{12} f(x) - 1 \, dx = -7\int_9^{12} f(x) \, dx + 7\int_9^{12} 1 \, dx


    2. if F(x) = \int_a^x f(t) dt , then F'(x) = f(x)
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  3. #3
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    Quote Originally Posted by skeeter View Post
    properties of definite integrals

    1. \int_6^{15} f(x) \, dx = \int_6^9 f(x) \, dx + \int_9^{12} f(x) \, dx + \int_{12}^{15} f(x) \, dx

    solve for \int_9^{12} f(x) \, dx ... you were given the values for all the other definite integrals.

    \int_{12}^9 7f(x) - 7 \, dx =

    7\int_{12}^9 f(x) - 1 \, dx = -7\int_9^{12} f(x) - 1 \, dx = -7\int_9^{12} f(x) \, dx + 7\int_9^{12} 1 \, dx


    2. if F(x) = \int_a^x f(t) dt , then F'(x) = f(x)
    So for the first part of number 1 i got = -3. so how do i plug this in to get the second part? I look at what you did for second part and still dont understand.. please explain more. Thanks
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  4. #4
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    Quote Originally Posted by Kayla_N View Post
    So for the first part of number 1 i got = -3. so how do i plug this in to get the second part? I look at what you did for second part and still dont understand.. please explain more. Thanks
    It is expected that you can substitute \int_{9}^{12} f(x) \, dx= -3 into -7\int_9^{12} f(x) \, dx + 7\int_9^{12} 1 \, dx.

    It is also expected that you can evaluate \int_9^{12} 1 \, dx.

    Please say where you get stuck trying to do these two things.
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