This was part of a test I took inclass and I bombed it... I need to know the right way to do it.Thank you.
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I really need someone to work this out so I can understand it.Thank you.
1. What is the area of the region bounded by the curves y = 2x^2 - 7 and y = 2/x between x=1 and x=3?
The answer I get, both by calculator and by hand, is 2ln(3) - 10/3. According to the test, it is 4ln(2) - 2ln(3) + 8. Even my calculator doesn't think that is equivalent.
This is from a Straighter Line test. They have been known to have some errors on their tests. If this is one of them, please inform me.
2. The second question is one I never really learned the way to do. I know how to get four points from it. But the rest of my methods seem convoluted. It is: what is the area of the parallelogram whose edges are the lines y = - 1/2 * x - 1, y = x + 2, y = - 1/2 x + 2, and y = x - 5/2. What is the way to do this? Or, is there a particularly efficient and quick way to do it?
These two questions are from Calculus I. I mention this in case it helps to contextualize what methods you would recommend I answer this with. The Straighter Line course I am taking is very bad in regards to presenting all the information you need to know--if fact, it doesn't--so I have had to pick up quite a few things on the side myself. I may not have learned what I am supposed to do with some of these situations. But, I think the first of the two questions may be the result of an error on the part of Straighter LIne.
Ah, so, thank you for any answers.
in the following problem i have x^2y^2+xsiny=4 i understand wemust use the product rule on both of these, and implicit diff.means use dx/dy whenever we find the dir of y.
this is the step i took, and i was wondering if it was right,and how do i solve for y' now?
