Basic Integration: Exercise 1

by Batool Akmal

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    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...

    About the Lecture

    The lecture Basic Integration: Exercise 1 by Batool Akmal is from the course Basic Integration.

    Author of lecture Basic Integration: Exercise 1

     Batool Akmal

    Batool Akmal

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