This week we started in on chapter 7. Our last chapter of the year! And guess what it starts with...more integrals!
7.1 is application of integrals. This is just basically what we've been doing, but the story problem version of it. Integrals have always been easy for me, and this is really no different. All we are doing is plugging in numbers we are given for velocity and acceleration and figuring out what they ask me. We also revisited the s'(t)=v(t) and v'(t)=a(t) rules. This helps is solve the problems we are given.
We also starting learning areas under the curve and how to set up and solve integrals when we have x=y(t). For the picture, my integral would look like this:
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∫ (1/4)x^2 - x dx Because (1/4)x^2 is always above x on this interval.
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I was so confused at first learning when x=y(t), but I just have to remind myself that the bounds for solving a certain function when integrating with y are the y values of the points of intersection!
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