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.
Hello, Latszer!
I'm guessing at what the problem said . . .
Exactly where is your difficulty?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 $
$\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 $
. . . $\displaystyle = \quad m\underbrace{\int^b_a\!\! g(x)\,dx}_{\text{This is 1}} \;+\; n^2\underbrace{\int^b_a[f(x)]^2dx}_{\text{This is 13}} \quad=\quad m + 13n^2$