integrate-each-function-by-using-the-table-in-appendix-d-int-sin-3-4-x-cos-3-4-x-d-x-2

Question

Integrate each function by using the table in Appendix $D$.
$$\int \sin ^{3} 4 x \cos ^{3} 4 x d x$$

Vipender Yadav · Accepted Answer

So here on this problem we need to evolve it an indefinite integral which is integration sign cube four X. Because I Ncube four X. B. X. And to evaluate this problem we need to refer the formulas that is given in the appendix city of the book. Now if you ever want formula which is given in the appendix T. And the formula is integration sign cube you Because in cuba you do you it is equals two signed to the power. M plus one. You consigned to the power and minus one. You divide by M plus N. Plus the uh this n minus one divided by empress in integration signed to the power. M. U. Consigned to the power and minus to you deal. So this is a form Lord that we&#x27;re going to use. We&#x27;ve elevated. Given in trouble. Now if you compare this formula with the given in trouble we can say that you we have four X. And do you would be equal to four dx. Here we have only dx. So to convert into a standard format we can do one thing. We can multiply it with four like this and divide it with four so that it will become four dx. And I&#x27;ve divided it was so that the integration doesn&#x27;t change. So now we can use exactly this formula to evaluate this ventricle. So and one more thing that we have M equals 23 and n is also three. Now let us put all the values in the formula. So it will be equals two. One by four. This one by four will remain as it is this one no sign to the power M plus and plus one. So um is we have a three. So it would be signed to the power for you. We have four X. So this would be four x times co sign and minus one would be to you. We have four X divide by this would become six so n plus one divide by employees. And so it would be three minus one is +22 divide by six integration signed to the power. M you sign em we have three sign cube you we have four X times consigned to the power and minus two. So three ministries one so you we have four X. So this would be consigned forex. And do you we have four dx next we&#x27;re going to evaluate this integral first so and to evaluate this integral we can use the same formula this one and in the second case we have M equals 23 and we have one. You we have four X. And do you would be equals two four D X. So I&#x27;m going to use the same formula and we&#x27;ll get this one is a cold too. We are evaluating this in google first. So let me write her. This is integration sign cube four X. Consigned four X times for the X. So we are evaluating the central so uh here and we have one. So if you plug in one hair this will become one management zero. So this whole town would be zero. So we have to consider only this time. So this would be assigned to the power M plus ones and plus one. We have force assigned to the power for you. We have four X divide where unpleasant, unpleasant and we have four. So this is the result. We don&#x27;t have to consider this time because this n minus one. So one cousin, one minus one is zero. So we can contribute to the consider only this one. So this is the village that we were playing And now you can plug it here. Surat will get so we can put it here and it will be equals to this one by four as it is. And here we have signed to the power forex. This is four X times cosine square four X divide by six plus. This would become 1/3 times this value. We have this much. So this is a sign to the power 44 X divide by four. Now can simplify this and finally we&#x27;ll get our answer to be won over 48 signed to the power four four x times to assign square four X plus one. Now we have to add the concept of integration. See because the integral is indefinite integral. So that is why we have to add this constancy. So this is a required answer for the given problem. I hope you have understood the problem. Thank you.

Sid Wan · Answer

can number turn we have into world sign acto the force cause I axed the eggs His guy If we take you to be sy ox two u equals cause I X People steal over there because I have so there&#x27;s integrate We can write us you two the force thiss guys do you bridge is just While we&#x27;re far view to the books from C Can&#x27;t substitute you buy Sign that.

Andrija Isakov · Answer

and this question will be finding the indefinite integral of 1/1 minus coast to the four Costa for X using integration tables, the integration table should have a formula for 1/1 minus coast of eight times X. Ray is a constant, and that formula would give minus one over a Times Co. Tensions of X over two, which is to extend our case. And of course, we need at the constant of integration because it&#x27;s indefinite integral, and that&#x27;s the answer.

Amy Jiang · Answer

Okay, so let&#x27;s first notice that we have coastline and fine, so we could probably use a Yusoff. Okay, I noticed that we have coast and with the power three. So I want to rewrite that as it even power. So I&#x27;m gonna split this up into Coastline Square directs. Find your power four X and then we have Rimini coastline of X, the X. Okay, so in this case, I want are you to be sign of X because I want our derivative to be co sign of xcx. So we have using to sign of come to you in its coast, on your back, the X. So if I&#x27;m going to take you to be able to sign a max, I&#x27;m gonna want to rewrite this coastline in terms of sign. Well, thankfully, we have argued Agrium intensity that states that co six quarterbacks plus times great of actually which one so solving for sine we have or actually solving for close, fine have equal to one minus sine squared. So it&#x27;s really that one minus sign square looks and then we have co sign. We&#x27;re actually fine. There are four x e. And now let&#x27;s replace what we have. I forgot. And we have a co signer by Yeah. Okay, so this is equal to one minus. You squared times you did about our four, and then we have Do you? Now it&#x27;s one of my end. This use your power for Okay, I&#x27;ll take in a robe. You have. You would just sign to the power of five X over five minus. Sign to the power of seven X over seven plus c. Okay, so we have the fall exclusion.

Alex Johnson · Answer

this problem. We&#x27;re gonna find the anti derivative of sign of X divided by the quantity Four minutes, Coast Innovex. We&#x27;re gonna use a u sub solve this. So first, let&#x27;s set Are you value to four minus co sign X and R D. You will be positive Sign of x d X And if we compare it to the original we we do have the four minus co sign X in the denominator and we have the sign of x d x a cz well from the numerator and at the end. So let&#x27;s set up our new integral in terms of the U values. So we have the integral the integral of one over you d you and the anti derivative is the natural log of the absolutely of you plus C. And we will change this back to have it in terms of X, which is the natural log of four minus co signed X plus C

K B · Answer

so this question to a value evaluate isn&#x27;t so what? We&#x27;re gonna be doing things like you be a sign of two ass us. So therefore, do you, in this case is gonna be equal to to co sign of two acts. This is our first thing that we&#x27;re gonna be doing. The next thing that we want to do here is then from this week, we&#x27;re also gonna find that D X is equal to co sign of two X next. And from this thing we confined that D X is you put a 1/2 to you one after you, we find this, but there&#x27;s two co side of two axes double coast. Now that we have these pieces of information, we&#x27;re gonna integrate and we&#x27;re gonna apply you to the power of end times. D&#x27;you is equal to you to the power of and plus one over on plus one plus our constant c. So, basically, we&#x27;re just gonna buy this tour for me. You know where we have 1/2. Well, here. Sometimes you could do you. Yeah, and then this is all time is equal to 1/2 times you to the fourth over four over for. And then after this, we&#x27;re gonna have to start off our constant seat farm. Now that we have this, we can simplify. And we know that you we can just say that this is you did before Over eight plus c reason for this being 1/2. We have to nominate your two and denominator force those multiply to get us that ate. So now what we&#x27;re gonna do is we&#x27;re gonna put in the answer back of the terms of acts. So remember that we had a beginning. We said that you was equal to sign of two acts. So let me put this back in. We get signed to the fourth, the two acts, because we have you to the power for years. That&#x27;s why I signed to the fore over a and sign the fourth of two X over eight plus seat. And this is gonna be our final answer.

Problem

Integrate each function by using the table in App…

Problem 43 Easy Difficulty

Integrate each function by using the table in Appendix $D$.
$$\int \sin ^{3} 4 x \cos ^{3} 4 x d x$$

Answer

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Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus

Anna Marie V.

Kayleah T.

Kristen K.

Michael J.

Precalculus Review - Intro

Functions on the Real Line - Overview

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Basic Technical Mathematics with Calculus

Anna Marie V.

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Allyn J. Washington, Richard S. EvansBasic Technical Mathematics with Calculus

Anna Marie V.

Kayleah T.

Kristen K.

Michael J.

Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus