Single-Function Properties Examples

If , what is ?

We can pull the constant out in front of the integral, then use what we were given.

If , what is ?

We switch the limits and switch the sign: 

The function f graphed below is even.

What is ?

Since

and f is even,

Let f (x) = sin x. What is ?

Since sin x is an odd function, this integral is 0.

We can also get a little more complicated and start combining rules.

If , what is ?

We need to switch back the limits and get the 4 out of the integrand. It doesn't matter which order we do this. If we switch the limits first, we get

 If we pull the 4 out first, we get