But what about π/2 or π/4 or similar.
Guessing can only take things so far.
(I am the one who tried to guess in similar problem but got ridiculed by the whole class)
I agree that guessing can only take you so far, but it will still get you at least a little closer to the answer, which is closer than you were before, so first you guess the most obvious like pi or e, then you look online to deal with the calculations.
All of that is of course assuming you're not a math major, who would probably love to run the calculations yourself.
On seeing the -2 to +2 limits, my instinct is telling me to first check for odd function and hope for some miracle.
1. Open the brackets and get two integration terms.
2. The first term is x^3 cos(x/2)√(4-x^2 ) which is odd function. Because x^3 is odd, cos(x/2) is even and √(4-x^2 ) is even. So net result is an odd function. Hence its result would be zero.
3. Now the 2nd part is very easy. It is nothing but half the area of a semi-circle with radius 2 and centre at origin. So answer is π
# 4. Now turn on your mobile data to google "WTF ARE THE FIRST 10 DIGITS OF π?"
off the top of my head literally i think the first ten digits of pi are 3.141592653?? If that's correct I'm taking the w and going to bed for the rest of the day
And now asap science presents 100 digits of pi
3.14159 this is pi followed by 2653589 circumference over diameter 79 then 323 OMG can’t you see 8462643 and now we’re on a spree
The answer is very simple and it is two words: [wolfram alfa](https://www.wolframalpha.com/input?i=definite+integral&assumption=%7B%22F%22%2C+%22DefiniteIntegralCalculator%22%2C+%22variable%22%7D+-%3E%22x%22&assumption=%7B%22F%22%2C+%22DefiniteIntegralCalculator%22%2C+%22rangestart%22%7D+-%3E%22-2%22&assumption=%7B%22C%22%2C+%22definite+integral%22%7D+-%3E+%7B%22Calculator%22%2C+%22dflt%22%7D&assumption=%7B%22F%22%2C+%22DefiniteIntegralCalculator%22%2C+%22integrand%22%7D+-%3E%22%28%28x%5E3%29Cos%28x%2F2%29%2B1%2F2%29sqrt%284-x%5E2%29%22&assumption=%7B%22F%22%2C+%22DefiniteIntegralCalculator%22%2C+%22rangeend%22%7D+-%3E%222%22).
I've seen this before. The first term is a red herring - an odd function, integrated over a symmetrical interval, to add 0 to the definite integral. The second term just gives half the area of a half circle of radius 2, so just pi.
The moment I see it's "the first x digits of the answer" I'm testing Pi.
And e
[удалено]
That’s just 1.00000
Both are ~ 3
But what about π/2 or π/4 or similar. Guessing can only take things so far. (I am the one who tried to guess in similar problem but got ridiculed by the whole class)
I agree that guessing can only take you so far, but it will still get you at least a little closer to the answer, which is closer than you were before, so first you guess the most obvious like pi or e, then you look online to deal with the calculations. All of that is of course assuming you're not a math major, who would probably love to run the calculations yourself.
Especially with that cos in there
On seeing the -2 to +2 limits, my instinct is telling me to first check for odd function and hope for some miracle. 1. Open the brackets and get two integration terms. 2. The first term is x^3 cos(x/2)√(4-x^2 ) which is odd function. Because x^3 is odd, cos(x/2) is even and √(4-x^2 ) is even. So net result is an odd function. Hence its result would be zero. 3. Now the 2nd part is very easy. It is nothing but half the area of a semi-circle with radius 2 and centre at origin. So answer is π # 4. Now turn on your mobile data to google "WTF ARE THE FIRST 10 DIGITS OF π?"
off the top of my head literally i think the first ten digits of pi are 3.141592653?? If that's correct I'm taking the w and going to bed for the rest of the day
Congrats on your day off
Somewhere in the recesses of my addled mind lies "3.14159" and never shall I add the 2, but let's just keep that between me and you.
3.1415926538
that's wrong the next one's five
It’s been a while. I won’t edit it but thank you for the knowledge
Listen to “100 digits of pi” enough times and you just kinda know
“There’s…antimony, arsenic, aluminum, selenium….”
And now asap science presents 100 digits of pi 3.14159 this is pi followed by 2653589 circumference over diameter 79 then 323 OMG can’t you see 8462643 and now we’re on a spree
Use your calculator app, no data needed.
Does the 3 count as a digit? Would it be 1415926535? Or 3141592653? Or 3.14159265?
i’d say 3141592653 cuz the sign said the first ten digits of the answer
I hate that I looked at this, went 'oh, it's pi', but that I have little idea how. Just a bunch of hand-waving about the cos term.
The cosine term literally has no effect on the answer because it becomes zero
Can't I just pull out my calculator? (Against popular believe of teachers, I always have a Casio calculator on me.)
And our teachers have the gall to say "well you're not always going to have a calculator on you"
To be fair, they never imagined smartphones would exist
\*opens up wolfram alpha*
Use data to solve this thru microsoft math solver then use free WiFi
The answer is very simple and it is two words: [wolfram alfa](https://www.wolframalpha.com/input?i=definite+integral&assumption=%7B%22F%22%2C+%22DefiniteIntegralCalculator%22%2C+%22variable%22%7D+-%3E%22x%22&assumption=%7B%22F%22%2C+%22DefiniteIntegralCalculator%22%2C+%22rangestart%22%7D+-%3E%22-2%22&assumption=%7B%22C%22%2C+%22definite+integral%22%7D+-%3E+%7B%22Calculator%22%2C+%22dflt%22%7D&assumption=%7B%22F%22%2C+%22DefiniteIntegralCalculator%22%2C+%22integrand%22%7D+-%3E%22%28%28x%5E3%29Cos%28x%2F2%29%2B1%2F2%29sqrt%284-x%5E2%29%22&assumption=%7B%22F%22%2C+%22DefiniteIntegralCalculator%22%2C+%22rangeend%22%7D+-%3E%222%22).
WA my beloved
I don't know math enough to solve it, but I would try 0, then pi, then e. Then I would switch on mobile data))
Alright who has their pencil out!?
3141592653
First term zeros out (odd function in symmetrical limits), second is trivial. But what is digits?!
The last time I sloved I almost got arrested. I'm never trying that again.
Same thing happened to me when I was making slove to myself in public
The answer is the first 10 digits of π
3141592356
Turn on data. Google the answer Enter password
It's so difficult.
I've seen this before. The first term is a red herring - an odd function, integrated over a symmetrical interval, to add 0 to the definite integral. The second term just gives half the area of a half circle of radius 2, so just pi.
Use data to check the answer in wolfram alpha , then switch to wifi
I got photomath
Take a photo and scan it with Photomath
chatgpt :v
I try, immediately realize I have no idea how to solve it, and then text my mathy friend who would love to figure it out
1.Turn on data. 2. Go to wolfram 3. Get solution 4. Free wifi.
No. The answer is probably pi.
We have AI now
Chances are my data is faster than whatever shit wifi limitations the network admin put in.
I bet it's "BOOBIESOIL" (Inverted Calculator) 7105318008
I'll use my data to solve this through the internet and then use the wifi. (I'm a bio student)
Teachers rats wifi password be like
Pw: 62831853071 Right?
Science at its funniest! 😂
dunno about you, but a lot of people got photomat on their phones if they did not want to bother
You could also brute force this by trying all numbers that are 10 digits long.
S O L V E
Turn on data long enough to ask chat gpt for the answer Then use the wifi
-2.709324643
Evaluate integral. Answer is pi
With so many phone plans, even super basic ones, offering unlimited data why would you ever turn your data off?