This specific integral is actually completely trivial First, this integral can be split in 2 parts: x^3*cos(x)sqrt(4 - x^2) and sqrt(4 - x^2)/2 The first part, the x^3*cos(x)sqrt(4 - x^2), is an odd function, meaning that its integral is 0 The other part is sqrt(4 - x^2)/2, which is a well known integral with value of pi
Ephesians 6:12 says, For we wrestle not against flesh and blood, but against principalities, against powers, against the rulers of the darkness of this world, against spiritual wickedness in high places. Jesus disrespected every religion, in John 14:6, Jesus saith unto him, I am the way, the truth, and the life: no man cometh unto the Father, but by me. We are not to be with any other religion. Because if we do, Matthew 6:24 says, No man can serve two masters: for either he will hate the one, and love the other; or else he will hold to the one, and despise the other. Ye cannot serve God and mammon. Don't pray for other religions.. But we are called to pray for one another in James 5:12 says, But above all things, my brethren, swear not, neither by heaven, neither by the earth, neither by any other oath: but let your yea be yea; and your nay, nay; lest ye fall into condemnation. Is any among you afflicted? let him pray. Is any merry? let him sing psalms. Jesus saves, God bless.😊
@@Heirloop yes, I believe you’re referring to symbolab, or one of the other bootleg offshoots. Those don’t work on hard integral equations though, like the one in the video.
This is an integral used in a Chinese university where the students must find the right 8 digits of this integral for the Wi-Fi password to get the Wi-Fi in the dining hall.
BRO JUST FORGOT EVERYTHING... THERE ITS WRITTEN WIFI password is the first digits of the answer... but password cant be of single digit... even if it is we can just put 9 try and you will get wifi.... LOL NO NEED TO SOLVE IT
@@coolcat-nq4mj yeah, and Pi Radians = 180 degrees that's the conversion Pi itself equals 3.1415... If you say Pi equals 180 degrees that would be like saying 100 = 62.1371 mph 100 what? 100 meters per second? 100 flapjacks per second? you haven't given a unit Radians is another unit just like Degrees, Radians is built upon the circumference of a circle being 2 times Pi (Tau) Radians, just like every 360 degrees is the circumference of a circle.
The worse part is he could have just used a direct theorem to solve the second broken integral instead of drawing a curve and taking half a circle, which would yield 0 when you put the limits 😭
@@CLASHERHEREjust saying, that’s a really REALLY bad way of understanding integration. What op meant is the dx is randomly put inside the function which makes 0 sense
No. All steps are correct. Reason : Integration is basically under the curve(one variable). So, for the 2nd term, he plotted the graph, and found the required area.
@@HimanshuHKKumaryeah but right at the beginning writes out the equation on the white board he removes the dx from under the square route. I guess he assumed this was a mistake made by the cafe
@@HimanshuHKKumar I think as the limit is -2 to +2 the x value would have been 0 and he would have removed it while adding as int/dx is x+c without limit but the limit is given
@@arsh_arora10Hello Radhe Krishna, My friend trigonometry is very easy just focus on your conceptual understanding and trigonometry will also be very very important in class 11 as well as in 12 so you please don't leave it😅. I love trigonometry that's why I am able to do integration very easily as compared to my classmates. This question is very simple just one has to apply properties of definite integrals and a formula of "integration of some of types" and you are done. And I also have my boards on 9 March 🫠
I can do this This whole maths is based on class 12 syllabus First you checked for odd and make its zero Then you checked it as even and applied the property of definite integral After that you applied the formula of integration This is easy one but looks hard
@@xinpingdonohoe3978it is possible to do in your head, but only if you know what to look for. I like this video though because it SHOWS the entire process. Edit: duplicate word
@@user-ot3tu1yb2j I guess that's true, but after enough integration the first thing you'll check for on a symmetric domain (like -2≤x≤2) is the parity of the function.
@@pramathhegde317where by parts...😅 There is direct formula applicable here ... 1/2√4-x² is an even function then integral can further be changed to 2 times that function limit 0→2
The dx is under the square root, so it is dx^(1/2). You calculated the full integral, but you were asked to do the half integral. And yes, this concept does exist (actually many different concepts of fractional calculus exist). A common one is the Riemann-Liouville-Differintegral formula.
Most of that function is even, and because of the limits being symmetrical, you can ignore the majority of it. You only need to integrate one half times the square root. Quick trig sub gives you pi. Work smarter not harder!
Easy way : u have divided the q. In 2 parts like he did and got 1 part as a odd integration f(x) =0 . Now for the 2nd part we can it as under root (2²+x²) and simple use the property of a²+x²dx =x/2•under root a²+x²+a²/2•sin-¹x/3
If you’re taking calculus then chances are you actually will use it. The people who ask this imbecilic question don’t usually aspire to more than grade school algebra.
@@coolguy-hu4ou there’s actually possible manipulations we can do because of the fact that the dx operator tends to 0. Bri the math guy did a cool video on this concept
@@coolguy-hu4ou Well, you can integrate with respect to a function, so it wouldn't be that much of a problem, except sqrt(x) isn't defined on [-2,0), so in this case such an integral wouldn't exist.
@@ilikechickennuggetssebee7238 Which is half-integral. Also: d(x^2) != dx^2 != (dx)^2 != d^2x. d(x^2) means you are differentiating over x^2 instead of x. dx^2 is the second differential of x. (dx)^2 is the square of the differential. d^2x is the second derivative of y multiplied by dy^2.
The integral can be easily solved mentally. The term with the cosine function is point-symmetric with respect to the origin due to the factor x^3. Because of the symmetric limits of integration, the integral over this part vanishes. What remains is the factor 1/2 and an integral over a semicircle with a radius of 2. The area of the circle is 4π. Thus, the area of the semicircle is 2π. Due to the factor 1/2 in the integral, the result is π.
@@listey but everyone knows pi Is 3.14 Everyone refers to pi as 3.14 In math when told to use pi, you use 3.14 If the calculator doesn't have a pi button or If you aren't using a calculator you don't write out pi you write out 3.14 The first digits It Is known across the board that 3.14 Is the first digits of pi Everyone knows that You are arguing for the sake of arguing rn You aren't helping at all
You could also know that the answer is pi because the sentence below the equation reads: “The WiFi password is the first digits of the answer” so we have an irrational number and you see cosine which is a trigonometric term and the first irrational number used in geometry that comes to your mind is pi
Bro this can be done in 3 steps If u separate x^3cos(x/2) root(4-x^2) and 1/2root(4-x^2), then first term will be zero as it's an odd function where limits are -2 to 2. And in second function simply use the formula of integration root(a^2-x^2). That will give the answer pi. It's basically a question of high school mathematics in India.
well, these are actually exactly the steps the guy uses to integrate this as well, just spelled out a bit (for dramatic effect I assume) except he doesn't use a memorised formula for the integral of root(a^2-x^2). why would you even learn that? you can just derive it geometrically if you really need it
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@@advikookie true jee aspirant ko pta hota h konsa question easy h konsa hard Isi ke liye vo 2 saal tayari karte h taki dekh ke hi pta lagaya ja sake konsa question hoga konsa nhi
I love how it says the password is “the first digits of the answer” without actually specifying how many, so even by solving it you still have to do trial and error 😅
Open Excel. Assign a cell with the variable name dx, and set it equal to a small number, like 0.001. Title the A-column with x. Let its first value be 2, and each following value to equal the above cell + dx. Stop when the A-column equals 2 Title the B-column with y. Type in the integrand as a formula, and replace x with a reference to the corresponding row in the A-column. Title the C-column with y*dx, and evaluate corresponding B-column reference times dx. Add up the C-column entries, excluding the first. The sum will approximate this integral.
X^3cosx/2 becomes 0 as symmetrical limits and x^3 is an odd function Just solve integration of 1/2(sqrt(4-x^2) as integration sqrt(a^2-x^2) is direct formula
The government should have these questions for free wifi, completely randomized calculus. If someone can do calculus, better than the average population, they're smart enough to pay for free wifi & society simply failed them if they don't get the money.
@@CaliRATZ proof. Without moving the dx btw. Also the reason why I say it's impossible is because it is wrong du to the definition. It's the same as x/0. You can write it, but it's just not defined.
I find it funny how I’ve seen this short multiple times but only now a couple week after taking my high school math finals did I realize that this is actually fairly simple
When integrating from a to b , we replace 'x' in the function for (a+b-x). If the resultant function is negative of the first, it implies that the function is odd, and it's integral is zero. If it comes out to be even, it can be further solved using standard results.
nahh... you can easily put one of 3 standard integrals underroot (a^2 - x^2) which equals to sin inv x/a something i cant bother to type whole formula but its a direct approach
The part inside the brackets is an odd function meaning f(x)=f(-x) Since the domain is -2 to 2 this part basically cancels itself out The square root is a half circle, (its like the pythagorean theorem, just a little changed) So its basically just "whats the area of a half circle with a radius of 2?"
Odd function gets equated to 0 because the limits are -2 to 2 and the remaining 1/2 √4-x² is direct formula based or you can solve it with the help of Graph by finding the Area under the curve of it. It looks terrifying but is very easy once you start solving it.
Just use integration from 0 to 2 f( x) + f (-x) u get the answer in a minute , the method in the video is too lengthy , but u taught me a new approach so thanks
