Integrate 3x*2 using limits of 3 and 2

(See whiteboard for step by step process) First, we write down the function we want to integrate (3x2), and include the limits at the top and bottom of our integration sign to show that it's a definite integral. The next step is to integrate the function itself: we do this by raising the power of each term in the function by one, and then dividing that term by the new power. We can see that this leaves us with x3. Notice that I've written this new function in square brackets with the limits outside - remember it's a definite integral. Next, we plug in our limits, and subtract the first function (using 3 as an input) from the second function (using 2 as an input). It's really important to put both functions in brackets here so we don't get our pluses and minuses confused, although for this example it's not so important because we only have one term. We end up with (27) - (8), which works out to 19. That's our final answer.