# Homework Help: In the set?

1. Jan 25, 2012

### Ted123

If G=the set of all continuous complex-valued functions on the interval [0,1] and $f,g \in G$ then is $$\displaystyle f(x) \int^1_0 g(t) \; dt - g(x) \int^1_0 f(t)\;dt$$ in G?

If H=the set of all differentiable complex-valued functions on the interval [0,1] and $f,g \in H$ then is $$fg' - gf'$$ in H?

2. Jan 25, 2012

### HallsofIvy

$\int_0^1 f(x) dx$ and $\int_0^1 g(x)dx$ are numbers so, knowing that f and g are continuous, what can you say about Af+ Bg for constants B and G?

The derivative of f'g+ fg' is f''g+ 2f'g'+ fg''. Knowing that f and g are differentiable what can you say about f'' and g''?

3. Jan 25, 2012

### Ted123

Got it. They're both still in the sets.

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