hi people welcome to my channel i'm c chamber jacob so i've got these two exam questions there is a and b so start with b i mean we start with a so you copy the expression that you've been given okay so once you copy there what are you supposed to do there are very simple rules that you must put into consideration rule number one check the powers that you have where the letter that you are expecting um has okay so in this case x as the power two so what are you supposed to do to this power add a one then you say minus okay where there is no letter and you are integrating there is only a number put the letter that you are expecting in this case we are expecting x so put x so now here what happens here there is two plus one so just get that thing the way it looks put it down like this okay are we done not yet we need to simplify so here we have six x when we say two plus one what are we getting is three here it's also three okay minus five x okay so now here we have to divide okay we know that three into 3 is 1 into 6 is the 2. so we have 2 x power 3 minus 5 x so to show that this is the integration and there is a constant we have to say plus the c always put a c you say plus c you can only avoid putting a c if you have the limits here and here so now there are no numbers here there are no limits you need to put a plus one so this is how you work out okay so let's try to check b what are we supposed to do on b on b copy also everything we say this is our step one we copy the way it looks so this is it what we have and what letter are we respecting it see at x so the next thing here now will be to um change the way it looks here okay whenever you see a fraction okay you see we have a fraction here and we have a fraction here now here there is a fraction and there is a letter that we are expecting it see down here so we cannot integrate the way it looks here so we need to change things using the laws of indices it will look like this this side will maintain because we have no letter down here there is only a number okay even here everything is okay on this but the problem is right here this x squared must be go on top so it will look like this it was the power 2 here it would be power negative 2 that's all okay so now at this point we can integrate so how do we now integrate the same procedure add a one okay so we add the one to this power there is already a two here okay don't forget these two so once we add there we divide by that like we did here okay we added and divide it so here we say minus 5 what power is here is 1 so plus 1 over the same that we have here okay here we say plus x okay there we have a one here we say plus one and we divide by what we have right here okay so now at this point we now need to be very smart if you have a fraction like this there is a number dope and the number below this whatever value you get here will be multiplied by the number that is the right here this is division so of 3 here we have a 4 over a 2 times a 4 because this thing will give us a 4 this is the 4 we're talking about right here okay minus 5 x power 2 over 2. when we add here we get a 2 here we get a 2. here we have uh plus x power 1 over negative 1. this one is giving us a negative 1 even here negative one good we're almost there so our next step here will now be to clean up okay so how do we clean up here we have three x power four over okay over eight because two times four is eight minus here we'll copy the way it looks over a two here we have something like this okay because negative if we divide this negative and the uh positive here will give us a a negative one can go into whatever is on top so this is what we remain with we even put plastic c so this is our solution thank you so much for watching kindly subscribe to my youtube channel and also if you need online tuitions you get in touch with me right here so let me write the number for you this is the number that you whatsapp me and i'll respond back to you bye bye