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

Find the value of the following integral.

$\displaystyle \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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- Nov 24th 2009, 02:31 PMLatszerWierd integral problem
Let the following be true. (all the stuff at the bottom.)

Find the value of the following integral.

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

That is all the problem tells me, thanks for any help. - Nov 24th 2009, 03:01 PMSoroban
Hello, Latszer!

I'mat what the problem said . . .*guessing*

Quote:

Given:

. . $\displaystyle \int^b_a f(x)\,dx \;=\;8$

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

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

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

Find the value of: .$\displaystyle \int_a^b \bigg(m\cdot g(x) + \left[n\cdot f(x)\right]^2\bigg)\,dx $

is your difficulty?*where*

$\displaystyle \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 $

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

- Nov 24th 2009, 03:10 PMLatszer
the problem says g(t) for the last two, I wrote it right.

- Nov 24th 2009, 03:12 PMJameson