Although I love the bits of Full Metal Jacket with the drill sergeant, I doubt he was that extreme with real recruits . Eg In our army it is a court martial offence for a drill sergeant to strike a recruit. Of course they found other, more creative ways to be cunts.
My first guess/attempt involved polynomial long division, but I failed. But I might have chosen poorly. I assume the pin is the coefficients of the x terms in descending order?
Evaluating the integral surely is not the solution, as the numerator (3x3-x2+2x-4) is negative in the range x∈ [0,1], while the denominator (sqrt(x2-3x+2)) is positive. The entire expression under the integral sign is bounded by the box x∈ [0,1] and
y∈ [-3.5,-0.5] (approximately) y∈ [-3.5,0]. Note that the expression is undetermined at x=1, where the numerator and demoninators both are zero (“zero divided by zero”). However, by employing l’Hôpital’s rule we can see that the integrand approaches zero in the limit x→0, so integrating should be OK. Solving the integral numerically yields approximately -2.98.
I solved the integral numerically using Python, as seen below.
Edit to add:
The integral is possible to solve, however the result is relatively nasty. You can do it online at https://www.integral-calculator.com/. Input the function and you get an analytical result. The antiderivative of the integrand is
which gives us a result for the definite integral of −2.981266944005536, which is the same as I got (to 14 digits) by doing a naïve numerical integration.
I have no idea. My level of math just requires competence in trigonometry, not this stuff, above my pay grade.
But I suspected those like you competent in this level of math would take it on. lol
I last time I passed maths was in grade 7. For years, I thought I just couldn’t do math, not smart enough.
When I was admitted to university as a mature age student, part of a course included symbolic logic. Couldn’t do it. My tutor very kindly gave me private lessons and I passed the open book exam at the end of the course… Turned out my problem was with the way I had been taught. IE incompetently .
Similar to my story. Barely scraped by in high school. A few years later and more mature, I graduated with a GPS of 4.0.
A little wiser, a lot more mature and motivated, and truly great instructors.
Me too. Yes and No. Was top of the class in English and history, but fell apart in exams, only managing B’s and C’s***. Finished high school at night.
At uni, straight A’s, except for logic in which I managed grade 1 pass.
Here we have public examinations in year 12. Grades are calculated by percentages. Eg say top 3% get A’s, lowest ?% fail. I’ve heard of GPS but don’t understand it. Sere public exam results determine if a person will be admitted to university and to what disciples. Eg Liberal arts have the lowest standards, and professions such as say Medicine, law and architecture have the highest .
My mate has a degree in pure mathematics. He’s a retired computer programmer. He regrets not doing law or medicine.
A friend’s daughter in England has a Phd in physics from Cambridge. At one point she complained to her mum that the course was very hard. Mum said “Oh that’s alright dear. Why don’t you do something easier, like medicine”
I was under the assumption from the story that the antiderivative would work out to something pretty; so I started with the assumption that it would be of the form Ax^4 + Bx^3 + Dx^2 + Ex^1 + c; with A, B, D, and E being integers with the digits of the pins being |A|, |B|, |D|, |E|. As you pointed out, that is not the case; and I made no progress after making that (bad) assumption.
Considering that the denominator is the square root of a non-square polynomial, it cannot be reduced to a pure fourth degree polynomial. Further, there is no obvious simple substitution you can make, nor is integration by parts an obvious solution to do it quickly. However, there is a way to see find a solution automatically. Paste function “(3x^3-x^2+2x-4)/sqrt(x^2-3x+2)” to the integrand box of the site I linked to earlier and hit the “Go!” button. Then, when the antiderivative has been computed, hit the “Show steps” button in the “Manual” integration with steps section. This reveals a solution that involves completing squares, and then doing a trigonometric substitution to get rid of the square root and get a sum of simpler trigonometric integrals.
That should read " STAUNCH AUSSIE Atheist"
PS: because his parents are also atheists, they throw the parasite out when he reaches 18.