First off we started with a few problems which you probably recognized from past units.
Find the area bound by the two curves:
To solve these, you must look at the graphs, and determine which function is above and which is below. Then you take the integral of the top function minus the bottom function. To find the interval, make the two functions equal each other and solve for x.
After that we discussed a problem where we are given a velocity function and asked to find the displacement, also known as net distance, and total distance travelled. The net distance is found by subtracting the negative integrals from the positive integrals. The total distance travelled is found by taking the integral of the absolute value of v(t).
That's all you need to know to do excercise 8.1.
Then we started to discuss how a 3 dimensional object is created by 'spinning' the function around the x axis (or y axis, but we didn't get into that just yet). We discussed how you can take many 'slices' of the solid, so thin that the width approaches zero. I guess we'll be expanding on this in class tomorrow.
The rest of the assigned homework includes the odd questions from 1-7 of exercise 8.2.
The scribe tomorrow shall be...... Danny.
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