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Math Help - Find lower bound of integral

  1. #1
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    Question Find lower bound of integral

    Suppose 3x+7= integral from a to x (f(t)dt) What is the value of a?

    I applied the fundamental theorem of calculus part 2 to get that f(x) = 3.

    Then, I applied the first part of the fundamental theorem to get that the integral from a to x of 3 dt = 3x - 3a.

    Looking at the solutions, it says that 3x - 3a = 3x + 7. Then you simply solve for a.

    I don't understand why this relationship is true. How is 3x - 3a equal to 3x + 7?
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  2. #2
    MHF Contributor
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    Re: Find lower bound of integral

    You've done all the hard stuff.

    3x+7 is given in the question as the value of the definite integral.

    You have calculated the same integral as having a numeric value of 3x-3a.


    So 3x+7 = 3x-3a. solve for a


    If you're still confused you are probably over-thinking the problem. You have two expressions for the same definite integral, so they must be equal.
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  3. #3
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    Re: Find lower bound of integral

    Thank you!
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