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Math Help - Integral Problem

  1. #1
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    Integral Problem

    Hello! I am a senior in high school who is taking AP Calculus. I'm stuck on this problem. I tried several methods to solve this, but couldn't match any of my answers with the choices. Any help would be wonderful. Thank you in advance!

    If \int^3_{0}f(x)dx=6 and \int^5_{3}f(x)dx=4, then \int^5_{0}(3+2f(x))dx=
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  2. #2
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    F(3) - F(0) = 6
    F(5) - F(3) = 4

    \int_{0}^{5} f(x)dx = F(5) - F(0) = 10

    Now they're just playing games from here.

    \int_{0}^{5}(3+2f(x))dx = \int_{0}^{5}3dx + \int_{0}^{5}2f(x)dx = 3 \int_{0}^{5}dx + 2\int_{0}^{5}f(x)dx
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    Hi derfleurer! Thank you so much for your help! And a quick response at that! I finally got an answer from the choices, which was 35. I understood everything you said. I'll be sure to remember this for future exams and problems!
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  4. #4
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    Quote Originally Posted by mamori View Post
    Hi derfleurer! Thank you so much for your help! And a quick response at that! I finally got an answer from the choices, which was 35. I understood everything you said. I'll be sure to remember this for future exams and problems!
    Quote Originally Posted by derfleurer View Post
    F(3) - F(0) = 6
    F(5) - F(3) = 4

    \int_{0}^{5} f(x)dx = F(5) - F(0) = 10

    Now they're just playing games from here.

    \int_{0}^{5}(3+2f(x))dx = \int_{0}^{5}3dx + \int_{0}^{5}2f(x)dx = 3 \int_{0}^{5}dx + 2\int_{0}^{5}f(x)dx
    A thing I might add without the use of antiderivatives is

    \int_{0}^{3}f(x)dx + \int_{3}^{5}f(x)dx = \int_{0}^{5}f(x)dx
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  5. #5
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    Do you have any idea how slow I am at typing LaTeX? =p
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  6. #6
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    Quote Originally Posted by derfleurer View Post
    Do you have any idea how slow I am at typing LaTeX? =p
    It gets better (besides a copy and paste works well). Did you notice that you can type the latex code and then highlight and then use the \Sigma in the tool bar?
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    Do you have any idea how pitifully JavaScript handles under IE5.5?Shoot me. =p
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