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We realize that if we integrate what is given in the clue, then we end up getting the integral in the question….

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Great work

So dy/dx is NOT a fraction, it is what is known as an operator. However, to simplify things in order to solve a separable differential equation, we can treat it as a fraction and bring every term with y and dy on one side, and every term with X and dx on the other. Then, we integrate both sides with respect to the variable on each side and we will be able to obtain some form of equation for y in terms of x, whether it be implicit or explicit!

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The uses of e are plenty in calculus, complex numbers, series expansions, analysis and even more advanced fields in mathematics!

The origins of e. Assume you start with $1 in your account. Then, you are told that you will get 50% interest on it, and it will be compounded twice a year. Of course, you take the deal. Then, you are told that in fact you will only get 25% interest on it, but compounded 4 times a year. You quickly realize that the more times you get the compound interest the better it is for you. In fact, this number is actually derived by getting an infinitely low amount of compound interest an infinite many times, assuming you start with $1 in your bank account. Hopefully the animation was able to show that well!

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Sometimes we have a fraction that is very ugly to deal with, and therefore we have to decompose it into two (or more) PARTIAL fractions. The way this is done depends on the order of the numerator and the denominator, and in this video we take a look at a specific example where the numerator is of order 0 and the denominator is of order 2. One use of decomposing into partial fractions is that it allows us to be able to integrate more complex functions!

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The first step is to follow the clue and take the derivative of the function they have given us. It will be apparent why soon. The main idea behind recurring integrals is that we don’t want to have to integrate many times- instead, we aim to find a formula that will give us any ‘n’th integral by just plugging in the number for n. Usually, it is difficult to obtain a formula like this on our own, so often we are given the formula but are told to prove that the formula is correct.

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What is integration by parts? The real answer is that it is probably the most powerful integration technique that is known to us, while another answer you might get is that it is the reverse product rule. Both are correct. In this animation, we take a look at the integral of xlnx with respect to x, and visually understand how the formula works with this particular example. Remember to like and follow for more maths content

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In case I’m going too quick let me explain how we got 1/4. We are trying to simplify 13/52, and we realize that they both share a common factor which is 13. Then, we divide both the numerator and the denominator by 13, and 13/13 gives us 1 in the numerator, while 52/13 gives us 4 in the denominator, hence giving us 1/4 as our final simplified fraction!

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Nice handwriting

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Thanks for this 🫡🫡

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Correction: When I add the two fractions at around 11:10, the answer is 31/40 and not 21/40.

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Wow. I never realised this. Thank you

I’m impressed

Good job

Perfect

Best explanation

Median is good when you have outliers, and mean is better when you don't. Thats what I go by anyway

The median is only guaranteed to belong to the data set if there are an odd number of items; otherwise, it's the average of the two center items.