# Area in shades region (Matlab)

1. Aug 11, 2014

### Maylis

This is a part matlab and part math question. I know for the shaded region, I would usually do
$A_{shaded} = \int_{inter(2)}^{inter(3)} f_{1}(x) \mathrm{d}x - \int_{inter(2)}^{inter(3)} f_{2}(x) \mathrm{d}x$

However, since it appears they want the function handle to be just one line, am I allowed to do

Code (Text):
fh = @(x) -0.1*x.^3 - 0.5*x.^2 - 2.2*x + 9
Since I can't make two integrals and just subtract them?

In other words, would it be correct to say
$A_{shaded} = \int_{inter(2)}^{inter(3)} (f_{1}(x)-f_{2}(x)) \mathrm{d}x$?

Last edited: Aug 11, 2014
2. Aug 12, 2014

### HallsofIvy

Yes, of course, that's correct. One of the first things you should learn about integrals is that they are "linear": $$\int_a^b (\alpha f+ \beta g) dx= \alpha\int_a^b f dx+ \beta \int_a^b g dx$$

Last edited by a moderator: Aug 12, 2014