1. ## 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.

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

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

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

3. the problem says g(t) for the last two, I wrote it right.

4. Originally Posted by Latszer
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?