Integration Method: Example 1

by Batool Akmal

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    Moving on to our second example. You may find this a little bit familiar because we've done this previously when we used the trapezium rule. So we applied the trapezium rule on this question with five ordinates and we found an area. Hopefully, we can now do this faster using integration and we should get a more accurate answer to what we got earlier with our approximation. Let's have a look at our integral. We have 0 to 1 and we have 3x plus 1 to the power of 2 dx. Right. This is a little bit more complicated than the previous question, because you think about it, when we were talking about differentiation, you have a function inside of a function. But we now have to integrate this. So, if you ever need to integrate something like this, you're still just trying to do the opposite of the chain rule. Let's talk about this for a moment. Let's make some space here. When you integrate this, you integrate the outside function first just as you did with differentiation. So when you integrate the outside function, you will get 3x plus 1 as it is without changing it, add 1 to the power and then divide by the new power. So that's pretty straightforward. But then remember, when we applied the chain rule, we multiplied it with the differential of the inside. So with the chain rule, we multiply it with the differential of the inside. What's the opposite of multiplication? It's division. So in this case, we're going to divide with the differential of the inside. So the differential of the inside function is 3, and instead we're going to divide it. So you can see that one of the 3's comes from the power, and the other 3...

    About the Lecture

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

    Author of lecture Integration Method: Example 1

     Batool Akmal

    Batool Akmal

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