So let's see how you got on with the
first set of integration questions.
Have a look at the first
exercise and the first question.
We're asked to integrate 5x
squared plus 3x minus 2dx.
Now remember what I said,
don’t worry about the dx,
it's just there saying,
"with respect to x."
So it's nothing really that needs
integrating or any sort of
mathematical stuff done to it.
So, let's have a go with
integrating where we're going to
integrate each individual term
nice and straightforward.
Remember the rules for integration; add 1
to the power and divide by a new power.
So, when I add 1 to the power of
X squared, I get 5x cubed over 3.
So remember to divide by the
new power, not the old one.
So these numbers
should be the same.
You then add 1 to the power of X to
the 1, that goes to 3x square over 2.
Do you remember what to
do with the constants?
So with differentiation,
the constants disappeared.
And in this case, remember to
multiply it with an x value.
So this is actually increasing
rather than going away.
So this becomes minus 2x.
And then don’t forget,
when you're dealing with indefinite
integration to put a plus C at the end.
You can find this plus C if you
knew X values and Y values.
You could have just substituted them in.
But as a general rule, when
we do indefinite integration,
we always put a plus C at the end t
o show that we appreciate that
there is a constant at the end.
That constant could be zero sometimes.
So it could be that there is no value
and that constant could be any number.
But still, to be fully correct,
just as we do with differentiation,
any constants go away,
we add a C to any indefinite integral.