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hi there now if you watched the first.video in this series we looked at.integrals that had this form here and.I've got three examples of integrals.that we discussed that had this form.just briefly there's a recap with this.first one f of X was X to the power 4 we.had something to the power 4 here that's.something we called G of X which was 2 X.cubed plus 1 and when you differentiated.it you got 6 x squared which was being.multiplied with F G of X and similarly I.leave it to you to have a look and check.that these two examples take on this.form but what happens if for instance.the constant changes let's say instead.of this constant 6 it's now a 7 and for.this one we had that the differential of.G of X was 20 X to the power 4 but we.change the constant not from a 20 now.but to say a 3 and in this last one we.had G of X was sine 3x when you're.differentiating it we have 3 cosine 3x.that constant 3 from the 3 cosine 3x.changes to another constant let's say 2.so how do we handle integrals that.essentially have this form but the.constant has changed we introduce a.constant here.well it's no different really from what.we were doing before remember it was.based around integrating f of X and then.replacing X with G of X but we've got.this next step here where we've got to.adjust for the constant a so I'll take.you slowly through each of these.examples let's start with number 1 now I.remember then.number one we've got f of X is X to the.power 4 it's based around X power 4.where that X is replaced with G of X 2x.cubed plus 1 and we've seen that if we.differentiate G of X we get 6x squared.but the constant has changed from a 6 to.a 7 so let's just suppose that it was 6x.squared here I showed you in the earlier.video that to do this then we integrate.f of X so we integrate X to the power 4.that's going to be 1/5 X to the power 5.but we replace the X with G of X which.is now 2 X cubed plus 1 and that's.raised to the power 5 and it would.finish there if that were a 6x squared.but what we need to do then is adjust.for that constant a we need to multiply.the 6 here by another constant to bring.us up to 7 and so what we do is that.that constant that adjusted constant.will be the 7 divided by the constant.that we've got here 6 7 6 and then we.got the constant of integration plus C.another way of looking at this constant.is just to look at it like this we've.got 6 x squared that's what we would.like to be there okay if it was the.previous type but we now need to.multiply it by this adjusting factor and.it's got to bring us to 7 x squared so.if we divide both sides by 6 x squared.you can see that that constant that we.adjust for is 7 6 so essentially we put.in the constant that we are given.we divide out the constant that we would.have had from differentiating G of X the.six in this case so all we need to do.now is just tidy this up 1/5 times 7 6.is just going to give us 7 over 37 30s.then of all of 2 X cubed plus 1 raised.to the power 5 plus the constant of.integration C ok let's just try the.second example now in the second example.it takes on this form remember f of X.now is e to the power X we've got e to.the power something that's something is.G of X which is 4 X to the power 5 and.if you differentiate G of X you get 20 X.to the power 4 but we've got 3 X to the.power 4 not the 20 X to power 4 so we.need to adjust for that constant so.again if it were a 20 there we would.integrate as we've done before that is.integrate f of X which is e to the X if.you integrate it you get e to the X so.we would have e to the power X you place.the X with G of X which is 4 X to the.power 5 and that would be it.Plus that constant of integration C but.we need to make an adjustment for this.constant 3 and what it is is we take the.3 and we divide out by the constant that.we had when we differentiated G of X the.20 so it's going to be 320 X again I'll.just do it on side here just in case.that causes any problems what we had.when we differentiated G of X was 20 X.to the power 4 so we've got 20 X to.power 4 we need to multiply it by a.constant in order to bring it to.three X to the power 4 and you can see.that by dividing both sides by 20 X to.the power 4 you get that constant of 3.twentieths which we put in here right.and in this last example what I've done.is taking this trigonometric type and in.this one it's based around f of X being.X to the power 5 and G of X is sine 3x.so we've got sine 3 X to the power 5.here and when you differentiate G of X.you get 3 cosine 3 X but instead of.having 3 cosine 3x here you see we've.got 2 cosine 3x so let's just imagine.that in the perfect world it was 3.cosine 3x there if it were then we would.integrate f of X first of all so.integrating X power 5 is 1/6 of X to the.power 6 but X is replaced with G of X so.that's going to be sine 3x and that.would all be raised to the power 6 but.I'm going to write 6 there and that.would be it but we've got to change the.3 here into a 2 so what we do is we take.the value we've got here the constant a.if you like up here which is 2 and.divide it by the constant that we've got.in the differential of G of X the 3 here.so that constant that we multiply by.then is 2/3 to make that adjustment and.we got the constant of integration and.doing it the way that I've done over.here it would just be simply I've got a.3 in G dash of X and I want to multiply.it by something to give.me that constant to and you can see that.it has to be two-thirds if we divide.both sides by three and so we've got it.there and just a question of cleaning.this up now one-sixth times two-thirds.that's going to be 2/18 which reduces.down to 1/9 so you've got 1/9 sine of 3x.or raised to the power 6 and then plus.that constant of integration C okay so I.hope that's giving you an idea then on.how you can work with this type of.integral by making an adjustment if.necessary with a constant and I must.stress at this point again because one.of the most common mistakes that I find.is that it only works when you've got to.make an adjustment for the constant you.can't make adjustments if that was safe.7x instead of 7x squared it must be.something x squared when you.differentiate the four X to the power.five it gives you 20 X to the power 4.some constant times X power 4 you can't.make an adjustment if that said just X Y.x squared or X cubed okay it must be.something X to the power 4 and so on.so do take care with that only adjust.for the constant now in my next video.I've got a summary exercise three more.questions that you might like to try.that are based on this idea so I would.strongly encourage you to have a go at.those.you.

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Form Af FAQs

Here are some frequently asked questions along with their answers to clear up the doubts that you might have.

Need help? Contact support

What is it like to be raised by an Indian father?

Incident 1 : ( 14 yrs old) Me: Mom I want to learn how to drive. Mom: you are underage, I will not allow. Wait for another 4 years. Dad listens to the entire conversation does not say a word. In the evening, me and dad step out to buy groceries. On the way back, stops car and says, come sit in the driver seat and himself jumps to the adjacent seat. Me: Why? Dad: You wanted to learn to drive, come I’ll teach. Don’t tell mummy. We did this for one month after which my dad let me drive the car when my mum was sitting. Incident 2: (During my 2nd semester in Engineering) I liked a girl and was looking at h Continue Reading

How can I fill out Google's intern host matching form to optimize my chances of receiving a match?

I was selected for a summer internship 2016. I tried to be very open while filling the preference form: I choose many products as my favorite products and I said I'm open about the team I want to join. I even was very open in the location and start date to get host matching interviews (I negotiated the start date in the interview until both me and my host were happy.) You could ask your recruiter to review your form (there are very cool and could help you a lot since they have a bigger experience). Do a search on the potential team. Before the interviews, try to find smart question that you are Continue Reading

What is the most beautiful thing your lover has done for you, e.g., a gift, a gesture, something that brought you together, et cetera?

My guy constantly amazes me; he's quick-witted and funny and so very interesting. Being with him is such a treat; I feel like the luckiest woman on earth because he chose me. But he's not given to overly-emotional displays of affection nor blatant declarations of love. So I've had to learn to spot the signs of how he really feels for me in the little things he does for me. This is one of the best. Boyfriend just started a new job. He is short on money, and I know for a fact that he doesn't have a lot of food in the fridge. We woke up early at his place to watch some movies, and he made me break Continue Reading

How do I fill out the form of DU CIC? I couldn't find the link to fill out the form.

Just register on the admission portal and during registration you will get an option for the entrance based course. Just register there. There is no separate form for DU CIC.

How difficult is it to transfer from one branch of the military to another (ex: AF to Navy)?

Depends. If you are in the middle of your contract, you have to fill out forms and give a pretty good reason for moving. You'll spend weeks waiting on some hot shot to sign it, by which point you should have what you're getting lined up. If it is at the end of your contract then it's easy because you're holding the cards. Just reenlist in the branch you want. Although noye that unless you lock in the EXACT job you had before, you will be going to a tech school/AIT.

What is a form 1067?

My favorite number is 9 and I believe that it is the coolest number out there. To begin, I would like to say that 42 is another amazing number, along with 7. Alright, so to show you all why 9 is the coolest number, I need to demonstrate something. Let’s take the first 10 multiples of 9: 09 18 27 36 45 54 63 72 81 90 Good? Now flip the numbers. Notice anything? As it turns out, the first ten multiples of 9 are a full-out palindrome. You may have already seen this, so let’s dig deeper! Nikola Tesla once stated “If you only knew the magnificence of the 3, 6 and 9, then you would have a key to the universe.” If you Continue Reading

What is SKT Air Force?

It is amazing. Because a) it’s a private plane and b) the food is amazing!! and c) there was a brief window when you could watch Air Force One on the inflight entertainment system onboard Air Force One but most important because d) it’s Air Force One! It’s not just being on the plane - it’s knowing that the plane is such a powerful symbol of the president’s role in America and America’s role in the world. So yeah, if you ever get a chance to fly on AF1, I suggest you take it.

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