Hi in this video we will discuss from the very beginning What is called an integral Hi integral is also called an antiderivative So it is highly recommended actually before understanding what an integral is to first understand well what a derivative is because it is very related to the song or not just whispers related What is a derivative What are the basic formulas for those who still don't really understand what a derivative is watch this video first the link is in the description so if we remember again for the derivative of the exponent y = x to the power of n it can be derived as Endi times x to the power of n min 1 so the exponent is multiplied in forward then minus one example for example we have x ^ 3X ^ 3 that if it is derived it becomes 3 x squared so three so times forward then minus one another example for example x ^ 3 + 5 it becomes 3 x squared because the constant if it is derived it becomes 0 another example the power of 3 minus 2 is also reduced to 3 x squared x ^ 3 + 10 is also reduced to 3 x squared this process from left to right we call it a derivative if we want to reverse from right to left we want to find the initial function before it is derived that we call it an integral Well so to be clear Why is integratedly called an antiderivative because It is the opposite so if we want to construct the formula x to the power of n it can be integrated into if earlier in the derivative the power is multiplied in front then minus 1 Now we try to use the opposite meaning the power is added by one first then we divide it forward Well earlier x ^ 3 x ^ 3 + 5 x to the power of 3 minus 2 x ^ 3 years 10 If it is derived it becomes 3 x squared 3 x squared if we want to return to the original function we return it to where we can take x ^ 3 x ^ 3 + 5 and so on so we lose the constant we can't track the initial constant how much they are added C to fill in the possibility of constants that we don't know that well integrals like this we call indefinite integrals yes because we don't know the value of c Well this is the first formula of the integral formula for x to the power of n we try an example yes for example if we have x ^ 3 Here the n becomes right is three So if we try to put it into the formula we will get one divided by 3 plus one multiplied by x ^ 3 + 1 we tidy it up it will be a quarter of x ^ 4 + C another example if we have x ^ 5 which makes n is five then we will get the result of one sixth x to the power of 6 plus C already if the Supra integral X ^ 3 how and this expression is not yet = x to the power of n we change it first to x to the power of min 3 means that the n is min3 by we can state okay one request plus one multiplied by x to the power of min 3 plus one we tidy it up we will get one minus 2 multiplied by x to the power of min 2 tanache another example of the integral of AKP x root x we can express as x to the power of half-half plus 13 both then we will get 1/32 multiplied by X ^ 3/2 the sign of c or 2 goes up we tidy it up to 2/3 x ^ 3/2 + c Well to make it easier for us to operate integrals there are some basic properties that are a little understood the first in integrals if there is addition or subtraction of two integral functions we can solve by integrating each of these functions what this means is that if we have x ^ 3 + x ^ 2 yes we can do this we can do x ^ 3 itself so a quarter x ^ 4 and Xbox both by themselves so a third x ^ 3 * we get the result 4x ^ 4 years one third hopefully 3 without C So if there is addition or subtraction of functions how to do it is just integral each second property is if for example there is a constant in front of the constant we just make it a multiplier after we integrate the function for example there are 4 x ^ 3 and 4 3 just rewrite x ^ 3 we integrate it to a quarter x ^ 4 we tidy it up to x ^ 4 plus C the next property is for the integral of a constant if it is drawn to integrate a constant the result is just we multiply X to KX for example the integral of 5dx Then the result is just 5 times x + c Well another example suppose if we have the integral 2x ^ 4 + 1 Well 2 means it will be a multiplier, then it will be multiplied by one fifth of x ^ 5 plus one, it will be integrated into X, so we get the result 25 x ^ 5 + x + c Hi, up Here are the basic properties of integrals that must be understood like this, it's still easy, right? Now let's try to enter another integral form, for example, we give the limit of a6p b-jak above and below, there are numbers, we call it sufficient limit and we read it from bottom to top, we read this integral as the integral from a to B for FX DX How do you do it? Zain, the integral that has a limit, for example, the result of the FX integral is F large X, then the integral from a to B for fx.gx is until FB minus Eva, so the difference is we substitute it into the function of the integral result, then we subtract it, the integral that has a limit, the result is no longer c, there is no constant whose value we don't know, so integration like this is called a definite integral, for example, we have an integral of 3 x squared, limited by 2-3 Let's just integrate 3x squared first will be x ^ 3 then enter the limit from 2-3 really we will get three to the power of 3 minus 2 ^ 3 we describe the result is 19 definite integral it also has basic properties integral properties that we discussed at the beginning of this pulse still apply yes these are the basic properties of integral Well for definite integral we add some more properties first if we integrate from a to a for an FX the result must be 0 for any function for example suppose we want to ask for dealing 3 x squared limited from 2-2 3 x squared the integral is x ^ 3 enter the limit later it will be two to the power of 3 minus 2 ^ 3 Again Then the result is zero this is logical because it whatever the result of the integral if the ends Eva less Eva again then it must be zero Well we go into the second property if there is an integral from to B for Effect that is the limit if we exchange the result we give minus example integral of 3 x squared limited from 3-2 earlier number 9 Kendari 2-3 now we are for 3-2 Then the result is x ^ 3 substituted in 2 and 3 becomes two to the power of 3 minus 3 to the power of three will get the result minus 19 this property is also maximence yes because initially FB minus Eva becomes Eva minus FB so yes the difference minus the final result well then the next property if we have an integral from a to B we can State it as an integral from a to how many first it's up to you for example tired C the problem right Plus the integral from C to B so if we look at the ends from a to B too The result will definitely be its security for example like number 9 earlier the integral from 2-3 for 3 x squared DX Well this we can just write as an integral cave for example up to five first for 3 x squared DX then we add the integral from 5-3 for 3 x squared DX for BTS from 2-5 later we will get 5 to the power of 3 minus 2 ^ 3 for the calf from 5-3 we will get three to the power of 3 minus 5 to the power of 3 we scribble neatly the final result is 19 so the final value No change yes both 19 this we call as the properties of definite integrals simple actually but this is very crucial especially for PTN test questions very often if there are definite integral questions the tracking is in these properties up to here understand yes Well now Let 's go into the indefinite integral questions again how to integrate in x ^ 3 divided by the root of x we can write it first as x ^ 3 divided by x to the power of half well here we can integrate in above like this Tegal below yes this is wrong because there is no integral property that can cover it we can do each work if it is addition like property number one this b if divided or multiplied it cannot be different from derivatives if you take down there is a division rule and a multiplication rule if there is no integral So how do we do it if we want to work on a problem like this well we have to break it down first we have to change it first for this problem we can be happy yes first x ^ 3 divided by x then half in the exponent if divided by the power minus 3 minus half is 5/2 so we can express this as xpangkah 52v so we can go back to the basic function x to the power of n here so this is 5/2 then the integral result is 27 times x to the power of 7/2 + C another example for example there is an integral of 2x times x squared + 2 well this also we can't do each of the work yes the integral of 2x is 2 Kris Middle x squared and the integral of x squared plus 2 is one third X ^ 3 + 2X this is wrong because multiplication is not covered in its nature which is covered only addition and subtraction which can be done each of the work so if there is Schalke Number 14 yes we have to explain it first this time for this case 2x times x squared y is 2 x ^ 3 2x times 2 is 4x 2x to the power of 3 is integrated into two times a quarter x ^ 4 4x becomes four times half x squared by we explain it into half x ^ 4 plus 2 x squared + C Okay so be careful here yes protein Which properties can we use? Understand the existing integral properties. Well, what if, for example, we have an integral problem of 2x times x squared + 2 ^ 5. Okay, problem number 14 is multiplication, so we can't integrate directly. Hi. So we have to explain it first, but the problem is that it's impossible for us to explain it because it's very long. School doesn't add 2, we raise it to the power of at least 5, so how do we do this problem? Well, if the form is like this, it's complicated, right? We can't use any properties and any formulas, so we have to manipulate the form. The technique for manipulating the form is so that in the end we want to use our basic formula. Techniques or methods. To manipulate the form, we call it integration techniques. Material related to integration techniques will probably be discussed in a separate video later because integration techniques are quite long, the story of integration techniques is essentially outsmarting How do we change the integral problem that we have, which has a complicated form, so we can express its form into our basic formula. There are various methods for integration techniques, there are substitution methods, there are partial integrals, and others, depending on what the problem is like. Later in this video, we will focus on What is an integral How is the formula formed what are the properties that we can use in integral operations and How to use it hopefully this video helps to understand the basics related to What is an integral Thank you for those who have liked subscribe Turn on the notification button please share this video if you growfat don't forget to leave a comment and if you want to learn more mathematics you can contact the contact in the description column