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Math Help - Integral problem

  1. #1
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    Integral problem

    I'm reviewing for math finals, and have run into a road block wit hthis problem:

    If the integral of f(x)dx from a to b equals a+2b, then the integral of
    (f(x) +5)dx from a to b equals what?

    I know how to do integrals when given the actual function, but have no idea how that +5 is going to affect the result in general. Can someone give me an idea of how to solve this kind of problem? The answer is supposed be 7b-5a. Thanks!
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  2. #2
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    Quote Originally Posted by abcocoa View Post
    I'm reviewing for math finals, and have run into a road block wit hthis problem:

    If the integral of f(x)dx from a to b equals a+2b, then the integral of
    (f(x) +5)dx from a to b equals what?

    I know how to do integrals when given the actual function, but have no idea how that +5 is going to affect the result in general. Can someone give me an idea of how to solve this kind of problem? The answer is supposed be 7b-5a. Thanks!
    \int_a^b f(x)+ 5 dx=\int_a^b f(x)dx+\int_1^b 5dx=a+2b+5(b-a)
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