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Math Help - Wierd integral problem

  1. #1
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    Wierd integral problem

    Let the following be true. (all the stuff at the bottom.)

    Find the value of the following integral.

    \int_a^b [m*g(x)+(n*f(x))^2]


    That is all the problem tells me, thanks for any help.
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  2. #2
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    Hello, Latszer!

    I'm guessing at what the problem said . . .


    Given:
    . . \int^b_a f(x)\,dx \;=\;8

    . . \int^b_a\bigg[f(x)\bigg]^2dx \;=\;13

    . . \int^b_a g(x)\,dx \;=\;1

    . . \int^b_a\bigg[g(x)\bigg]^2dx \;=\;2


    Find the value of: . \int_a^b \bigg(m\cdot g(x) + \left[n\cdot f(x)\right]^2\bigg)\,dx
    Exactly where is your difficulty?


    \int^b_a \bigg( m\cdot g(x) + [n\cdot f(x)]^2\bigg)\,dx \quad=\quad \int^b_a\bigg(m\cdot g(x) + n^2\cdot [f(x)]^2 \bigg)\,dx

    . . . = \quad m\underbrace{\int^b_a\!\! g(x)\,dx}_{\text{This is 1}} \;+\; n^2\underbrace{\int^b_a[f(x)]^2dx}_{\text{This is 13}} \quad=\quad m + 13n^2

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  3. #3
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    the problem says g(t) for the last two, I wrote it right.
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  4. #4
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    Quote Originally Posted by Latszer View Post
    the problem says g(t) for the last two, I wrote it right.
    Then there must be some way to express g(x) that isn't given in your post. Otherwise Soroban gave the right answer. If you didn't make a typo the problem doesn't make sense, do you see why?
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