Basic Integration: Exercise 1

by Batool Akmal

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    00:00 So let's see how you got on with the first set of integration questions.

    00:05 Have a look at the first exercise and the first question.

    00:09 We're asked to integrate 5x squared plus 3x minus 2dx.

    00:18 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.

    00:30 So, let's have a go with integrating where we're going to integrate each individual term nice and straightforward.

    00:35 Remember the rules for integration; add 1 to the power and divide by a new power.

    00:40 So, when I add 1 to the power of X squared, I get 5x cubed over 3.

    00:47 So remember to divide by the new power, not the old one.

    00:50 So these numbers should be the same.

    00:52 You then add 1 to the power of X to the 1, that goes to 3x square over 2.

    01:00 Do you remember what to do with the constants? So with differentiation, the constants disappeared.

    01:05 And in this case, remember to multiply it with an x value.

    01:10 So this is actually increasing rather than going away.

    01:13 So this becomes minus 2x.

    01:16 And then don’t forget, when you're dealing with indefinite integration to put a plus C at the end.

    01:22 You can find this plus C if you knew X values and Y values.

    01:26 You could have just substituted them in.

    01:28 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.

    01:37 That constant could be zero sometimes.

    01:39 So it could be that there is no value and that constant could be any number.

    01:43 But still, to be fully correct, just as we do with differentiation, any constants go away, we add a C to any indefinite integral.

    About the Lecture

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

    Included Quiz Questions

    1. (2/3)x³ + (1/2)x² + 7x + c
    2. (2/3)x³ + (1/2)x +(7/2)x + c
    3. (2/3)x³ + (1/2)x + 7x
    4. 2x³ + x + 7x + c
    5. (1/3)x³ + (1/2)x² + 7x + c
    1. (1/2) x^4 + (1/3) x³ + c
    2. (1/4) x^4 + (1/3) x³ + c
    3. (1/4) x^4 + (1/3) x³
    4. (1/2) x ^ 4 + (2/3) x² + c
    5. (1/2) x ^ 4 + (1/3) x² + c

    Author of lecture Basic Integration: Exercise 1

     Batool Akmal

    Batool Akmal

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